Search results for: generalized differential quadrature method

Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: S. O. Oyamakin, A. U. Chukwu

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Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, Richard's, stochastic

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points

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Authors: Nadia Chagtmi, Nejla Rejab, Noureddine Boulejfen

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This paper presents a calibration approach based on artificial neural networks (ANN) to determine the envelop signal (I+jQ) of a six-port based receiver (SPR). The memory effects called also dynamic behavior and the nonlinearity brought by diode based power detector have been taken into consideration by the ANN. Experimental set-up has been performed to validate the efficiency of this method. The efficiency of this approach has been confirmed by the obtained results in terms of waveforms. Moreover, the obtained error vector magnitude (EVM) and the mean absolute error (MAE) have been calculated in order to confirm and to test the ANN’s performance to achieve I/Q recovery using the output voltage detected by the power based detector. The baseband signal has been recovered using ANN with EVMs no higher than 1 % and an MAE no higher than 17, 26 for the SPR excited different type of signals such QAM (quadrature amplitude modulation) and LTE (Long Term Evolution).

Keywords: six-port based receiver; calibration, nonlinearity, memory effect, artificial neural network

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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: Vijay Kumar Singh, Pooja Kushwaha, Prabhat Ranjan, Krishna Kumar Ojha, Jitendra Kumar

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Present day high-throughput genomic technologies, NGS/microarrays, are producing large volume of data that require improved analysis methods to make sense of the data. The correlation between genes and samples has been regularly used to gain insight into many biological phenomena including, but not limited to, co-expression/co-regulation, gene regulatory networks, clustering and pattern identification. However, presence of outliers and violation of assumptions underlying Pearson correlation is frequent and may distort the actual correlation between the genes and lead to spurious conclusions. Here, we report a method to measure the strength of association between genes. The method assumes that the expression values of a gene are Bernoulli random variables whose outcome depends on the sample being probed. The method considers the two genes as uncorrelated if the number of sample with same outcome for both the genes (Ns) is equal to certainly expected number (Es). The extent of correlation depends on how far Ns can deviate from the Es. The method does not assume normality for the parent population, fairly unaffected by the presence of outliers, can be applied to qualitative data and it uses the binomial distribution to assess the significance of association. At this stage, we would not claim about the superiority of the method over other existing correlation methods, but our method could be another way of calculating correlation in addition to existing methods. The method uses binomial distribution, which has not been used until yet, to assess the significance of association between two variables. We are evaluating the performance of our method on NGS/microarray data, which is noisy and pierce by the outliers, to see if our method can differentiate between spurious and actual correlation. While working with the method, it has not escaped our notice that the method could also be generalized to measure the association of more than two variables which has been proven difficult with the existing methods.

Keywords: binomial distribution, correlation, microarray, outliers, transcriptome

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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: 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: Yurii Bloshko, Oksana Olar

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This paper presents the analysis of 6 different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms

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Authors: Neslihan Genckal, Reha Gursoy, Vedat Z. Dogan

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In this study, dynamic responses of composite plates on elastic foundations subjected to impact and moving loads are investigated. The first order shear deformation (FSDT) theory is used for moderately thick plates. Pasternak-type (two-parameter) elastic foundation is assumed. Elastic foundation effects are integrated into the governing equations. It is assumed that plate is first hit by a mass as an impact type loading then the mass continues to move on the composite plate as a distributed moving loading, which resembles the aircraft landing on airport pavements. Impact and moving loadings are modeled by a mass-spring-damper system with a wheel. The wheel is assumed to be continuously in contact with the plate after impact. The governing partial differential equations of motion for displacements are converted into the ordinary differential equations in the time domain by using Galerkin’s method. Then, these sets of equations are solved by using the Runge-Kutta method. Several parameters such as vertical and horizontal velocities of the aircraft, volume fractions of the steel rebar in the reinforced concrete layer, and the different touchdown locations of the aircraft tire on the runway are considered in the numerical simulation. The results are compared with those of the ABAQUS, which is a commercial finite element code.

Keywords: elastic foundation, impact, moving load, thick plate

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Authors: A. M. T. Jacinto, M.O. Osi

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Tamarind has various medicinal properties among which is its antibacterial property. Its bark contains saponins, alkaloids, sesquiterpenes and tannins. It is rich in phlobapenes which is responsible for antibacterial property. The objective of the study was to determine which bark will produce the highest antibacterial property, develop it into a topical cream and evaluate its quality and characteristics. Powdered barks of Tamarind were extracted by soxhlet method using 70% acetone. Stem bark produced a higher yield than trunk bark (5.85 g vs. 4.73 g). It was found that the trunk bark was more sensitive than stem bark to microorganisms namely Staphylococcus aureus, Corynebacterium minutissimum, and Streptococcus spp. Sensitivity of trunk bark can be attributed to a more developed phytoconstituents. Dermal sensitization test on both sexes of rabbits using the following concentrations: 100%, 40% and 20% of extract showed that Tamarind has no irritating property and therefore safe for formulation into an antibacterial cream. Excipients used for formulation such as methyl paraben, propyl paraben, stearyl alcohol and white petrolatum were compatible with the Tamarind acetone extract through Differential Scanning Calorimetry except sodium lauryl sulfate that exhibited crystallization when subjected at 200˚C. The method of manufacture used in cream is fusion, therefore strict compliance of processing temperature should be observed to prevent polymorphism. Quality control tests of formulated cream based on USP 30 and Philippine Pharmacopeia were satisfactory.

Keywords: antibacterial, differential scanning calorimetry, tannins, dermal sensitization

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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: Yaping Zhao

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In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: Jafar Khodagholizadeh

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In this talk, we study the tensor mode equation of perturbation in the presence of nonzero $-\Lambda$ as dark energy, whose dynamic nature depends on the Hubble parameter $ H$ and/or its time derivative. Dark energy, according to the total vacuum contribution, has little effect during the radiation-dominated era, but it reduces the squared amplitude of gravitational waves (GWs) up to $60\%$ for the wavelengths that enter the horizon during the matter-dominated era. Moreover, the observations bound on dark energy models, such as running vacuum model (RVM), generalized running vacuum model (GRVM), and generalized running vacuum subcase (GRVS), are effective in reducing the GWs’ amplitude. Although this effect is less for the wavelengths that enter the horizon at later times, this reduction is stable and permanent.

Keywords: gravitational waves, dark energy, GW's amplitude, all stage universe

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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: Abdelaziz Ghrib, Samir Hattali, Mouloud Ghrib, Mohamed Lamine Aouissia, David Ruch

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In the present study, the solid solutions with a chemical composition of Zr0.8Y0.2-xLaxO2 (x=0, 0.1, 0.2) were synthesized via two routes, by hydrothermal method using NaOH as precipitating agent at 230°C for 15h and by the sol–gel process using citric acid as complexing agent. Compounds have been characterized by powder X-ray diffraction (XRD), Scanning Electron Microscopy (SEM), Thermo gravimetric Analysis (TGA) and Differential Thermal Analysis (DTA) techniques for appropriate characterization of the distinct thermal events occurring during synthesis. All the compounds crystallize in cubic fluorite structure, as indicated by X-ray diffraction studie. The microstructure of oxides synthesized by sol-gel showed porosity that increased with the lanthanum La3+ contents compared to hydrothermal method which gives a single crystal oxide.

Keywords: oxide, hydrothermal, rare earth, solubility, sol-gel, ternary mixture

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Authors: Noora Al-Shanfari, M. Mazharul Islam

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The cumulative incidence function (CIF) is a fundamental approach for analyzing survival data in the presence of competing risks, which estimates the marginal probability for each competing event. Parametric modeling of CIF has the advantage of fitting various shapes of CIF and estimates the impact of covariates with maximum efficiency. To calculate the total CIF's covariate influence using a parametric model., it is essential to parametrize the baseline of the CIF. As the CIF is an improper function by nature, it is necessary to utilize an improper distribution when applying parametric models. The Gompertz distribution, which is an improper distribution, is limited in its applicability as it only accounts for monotone hazard shapes. The generalized Gompertz distribution, however, can adapt to a wider range of hazard shapes, including unimodal, bathtub, and monotonic increasing or decreasing hazard shapes. In this paper, the generalized Gompertz distribution is used to parametrize the baseline of the CIF, and the parameters of the proposed model are estimated using the maximum likelihood approach. The proposed model is compared with the existing Gompertz model using the Akaike information criterion. Appropriate statistical test procedures and model-fitting criteria will be used to test the adequacy of the model. Both models are applied to the ‘colon’ dataset, which is available in the “biostat3” package in R.

Keywords: competing risks, cumulative incidence function, improper distribution, parametric modeling, survival analysis

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Authors: M. R. Akbari, P. Soleimani, R. Khalili, Sara Akbari

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Analyzing and modeling the vibrational behavior of arched bridges during the earthquake in order to decrease the exerted damages to the structure is a very hard task to do. This item has been done analytically in the present paper for the first time. Due to the importance of building arched bridges as a great structure in the human being civilization and its specifications such as transferring vertical loads to its arcs and the lack of bending moments and shearing forces, this case study is devoted to this special issue. Here, the nonlinear vibration of arched bridges has been modeled and simulated by an arched beam with harmonic vertical loads and its behavior has been investigated by analyzing a nonlinear partial differential equation governing the system. It is notable that the procedure has been done analytically by AGM (Akbari, Ganji Method). Furthermore, comparisons have been made between the obtained results by numerical Method (rkf-45) and AGM in order to assess the scientific validity.

Keywords: new method (AGM), arched beam bridges, angular frequency, harmonic loads

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Authors: Afsaneh Mohammadnejad, Marianne Nygaard, Jan Baumbach, Shuxia Li, Weilong Li, Jesper Lund, Jacob v. B. Hjelmborg, Lene Christensen, Qihua Tan

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Cognitive impairment in the elderly is a key issue affecting the quality of life. Despite a strong genetic background in cognition, only a limited number of single nucleotide polymorphisms (SNPs) have been found. These explain a small proportion of the genetic component of cognitive function, thus leaving a large proportion unaccounted for. We hypothesize that one reason for this missing heritability is the misspecified modeling in data analysis concerning phenotype distribution as well as the relationship between SNP dosage and the phenotype of interest. In an attempt to overcome these issues, we introduced a model-free method based on the generalized correlation coefficient (GCC) in a genome-wide association study (GWAS) of cognitive function in twin samples and compared its performance with two popular linear regression models. The GCC-based GWAS identified two genome-wide significant (P-value < 5e-8) SNPs; rs2904650 near ZDHHC2 on chromosome 8 and rs111256489 near CD6 on chromosome 11. The kinship model also detected two genome-wide significant SNPs, rs112169253 on chromosome 4 and rs17417920 on chromosome 7, whereas no genome-wide significant SNPs were found by the linear mixed model (LME). Compared to the linear models, more meaningful biological pathways like GABA receptor activation, ion channel transport, neuroactive ligand-receptor interaction, and the renin-angiotensin system were found to be enriched by SNPs from GCC. The GCC model outperformed the linear regression models by identifying more genome-wide significant genetic variants and more meaningful biological pathways related to cognitive function. Moreover, GCC-based GWAS was robust in handling genetically related twin samples, which is an important feature in handling genetic confounding in association studies.

Keywords: cognition, generalized correlation coefficient, GWAS, twins

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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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Authors: Gitanjali Pagare, Hansa Devi, S. P. Sanyal

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Full-potential linearized augmented plane wave (FLAPW) method has been employed within the generalized gradient approximation (GGA) and local spin density approximation (LSDA) as the exchange correlation potential to investigate elastic properties of LaX (X = Cd and Hg) in their B2-type (CsCl) crystal structure. The calculated ground state properties such as lattice constant (a0), bulk modulus (B) and pressure derivative of bulk modulus (B') agree well with the available experimental results. The second order elastic constants (C11, C12 and C44) have been calculated. The ductility or brittleness of these intermetallic compounds is predicted by using Pugh’s rule B/GH and Cauchy’s pressure (C12-C44). The calculated results indicate that LaHg is the ductile whereas LaCd is brittle in nature.

Keywords: ductility/brittleness, elastic constants, equation of states, FP-LAPW method, intermetallics

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Authors: Zulfiqar Ali, Umar Saleem, Muhammad Junaid, Rizwan Tahir

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Gulzar Mahal is a heritage site located in the city of Bahawalpur, Pakistan. The site is under a process of degradation, as cracks are appearing on the walls, roofs, and floor around the building due to differential settlement. To preserve the integrity of the structure, a geotechnical distress evaluation was carried out to evaluate the causal factors and recommend remediation measures. The research involved the characterization of the problematic soil and analysis of the observed distress with respect to the geotechnical properties. Both conventional lab and field tests were used in conjunction with the unconventional techniques like; Electrical Resistivity Tomography (ERT) and FEA. The temporal, geophysical and geotechnical evaluations have concluded that the foundation soil over the past was subjected to variations in the land use, poor drainage patterns, overloading and fluctuations in groundwater table all contributing to the differential settlements manifesting in the form of the visible shear crack across the length and breadth of the building.

Keywords: differential settlement, distress evaluation, finite element analysis, Gulzar Mahal

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Authors: Kwabena Asare, Ezekiel N. N. Nortey, Felix O. Mettle

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Modelling of extreme events has always been of interest in fields such as hydrology and meteorology. However, after the recent global financial crises, appropriate models for modelling of such rare events leading to these crises have become quite essential in the finance and risk management fields. This paper models the extreme values of the Ghana Stock Exchange All-Shares indices (2000-2010) by applying the Extreme Value Theory to fit a model to the tails of the daily stock returns data. A conditional approach of the EVT was preferred and hence an ARMA-GARCH model was fitted to the data to correct for the effects of autocorrelation and conditional heteroscedastic terms present in the returns series, before EVT method was applied. The Peak Over Threshold (POT) approach of the EVT, which fits a Generalized Pareto Distribution (GPD) model to excesses above a certain selected threshold, was employed. Maximum likelihood estimates of the model parameters were obtained and the model’s goodness of fit was assessed graphically using Q-Q, P-P and density plots. The findings indicate that the GPD provides an adequate fit to the data of excesses. The size of the extreme daily Ghanaian stock market movements were then computed using the Value at Risk (VaR) and Expected Shortfall (ES) risk measures at some high quantiles, based on the fitted GPD model.

Keywords: extreme value theory, expected shortfall, generalized pareto distribution, peak over threshold, value at risk

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Authors: Zhi Zhang, Liling Cao, Seyedbabak Momenzadeh, Lisa Davey

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Reinforced concrete (RC) flat slab-column systems are commonly used in residential or office buildings, as the flat slab provides efficient clearance resulting in more stories at a given height than regular reinforced concrete beam-slab system. Punching shear of slab-column joints is a critical component of two-way reinforced concrete flat slab design. The unbalanced moment at the joint is transferred via slab moment and shear forces. ACI 318 provides an equation to evaluate the punching shear under the design load. It is important to note that the design code considers gravity and environmental load when considering the design load combinations, while it does not consider the effect from differential foundation settlement, which may be a governing load condition for the slab design. This paper describes how prestressed reinforced concrete slab punching shear is evaluated based on ACI 318 provisions and finite element analysis. A prestressed reinforced concrete slab under differential settlements is studied using the finite element modeling methodology. The punching shear check equation is explained. The methodology to extract data for punching shear check from the finite element model is described and correlated with the corresponding code provisions. The study indicates that the finite element analysis results should be carefully reviewed and processed in order to perform accurate punching shear evaluation. Conclusions are made based on the case studies to help engineers understand the punching shear behavior in prestressed and non-prestressed reinforced concrete slabs.

Keywords: differential settlement, finite element model, prestressed reinforced concrete slab, punching shear

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Authors: Habtamu Garoma Debela, Gemechis File Duressa

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In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

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Authors: Win Ko Ko, A. N. Temnov

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The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.

Keywords: nonlinear oscillations, two-layered liquid, instability region, hydrodynamic coefficients, resonance frequency

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Authors: Ekaterina Sánchez Romero, Emily Gabriela Aguirre Herrera, Sandra Luz Espinoza Esquerra, Jorge García Campos

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Female, 7 months old, daughter of a mother with anemia during pregnancy, with no history of atopy in the family, since birth she presents with recurrent dermatological and gastrointestinal infections, chronically treated for recurrent diaper dermatitis. At 6 months of age, she begins with generalized pallor, hyperpigmentation in hands and feet, smooth tongue, psychomotor retardation with lack of head support, sedation, and hypoactivity. She was referred to our hospital for a fever of 38°C, severe diaper rash, and pancytopenia with HB 9.3, platelets 38000, neutrophils 0.39 MCV: 86.80 high for her age. The approach was initiated to rule out myeloproliferative syndrome, with negative immunohistochemical results of bone marrow aspirate; during her stay, she presented neurological regression, lack of sucking, and focal seizures. CT scan showed cortical atrophy. The patient was diagnosed with primary immunodeficiency due to history; gamma globulin was administered without improvement with normal results of immunoglobulins and metabolic screening. When dermatological and neurological diagnoses were ruled out as the primary cause, a nutritional factor was evaluated, and a therapeutic trial was started with the administration of vitamin B12 and zinc, presenting clinical neurological improvement and resolution of pancytopenia in 2 months. It was decided to continue outpatient management. Discussion: We present a patient with neurological, dermatological involvement, and pancytopenia, so the most common differential diagnoses in this population were ruled out. Vitamin B12 deficiency is an uncommon entity. Due to maternal and clinical history, a therapeutic trial was started resulting in an improvement. Conclusion: VitaminB12 deficiency should be considered one of the differential diagnoses in the approach to pancytopenia with megaloblastic anemia associated with dermatologic and neurologic manifestations. Early treatment can reduce irreversible damage in these patients.

Keywords: vitamin B12 deficiency, pediatrics, pancytopenia, diaper dermatitis

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Authors: Ishit Sheth, Chandrasekhar Jinendran, Chinmaya Ranjan Sahu

Abstract:

A fourteen degree of freedom (DOF) ride and handling control mathematical model is developed for a car using generalized boltzmann hamel equation which will create a basis for design of ride and handling controller. Mathematical model developed yield equations of motion for non-holonomic constrained systems in quasi-coordinates. The governing differential equation developed integrates ride and handling control of car. Model-based systems engineering approach is implemented for simulation using matlab/simulink, vehicle’s response in different DOF is examined and later validated using commercial software (ADAMS). This manuscript involves detailed derivation of full car vehicle model which provides response in longitudinal, lateral and yaw motion to demonstrate the advantages of the developed model over the existing dynamic model. The dynamic behaviour of the developed ride and handling model is simulated for different road conditions.

Keywords: Full Vehicle Model, MBSE, Non Holonomic Constraints, Boltzmann Hamel Equation

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Authors: Yilmaz Simsek

Abstract:

In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

Procedia PDF Downloads 256