Flow and Heat Transfer Analysis of Copper-Water Nanofluid with Temperature Dependent Viscosity past a Riga Plate
Flow of electrically conducting nanofluids is of pivotal importance in countless industrial and medical appliances. Fluctuations in thermophysical properties of such fluids due to variations in temperature have not received due attention in the available literature. Present investigation aims to fill this void by analyzing the flow of copper-water nanofluid with temperature dependent viscosity past a Riga plate. Strong wall suction and viscous dissipation have also been taken into account. Numerical solutions for the resulting nonlinear system have been obtained. Results are presented in the graphical and tabular format in order to facilitate the physical analysis. An estimated expression for skin friction coefficient and Nusselt number are obtained by performing linear regression on numerical data for embedded parameters. Results indicate that the temperature dependent viscosity alters the velocity, as well as the temperature of the nanofluid and, is of considerable importance in the processes where high accuracy is desired. Addition of copper nanoparticles makes the momentum boundary layer thinner whereas viscosity parameter does not affect the boundary layer thickness. Moreover, the regression expressions indicate that magnitude of rate of change in effective skin friction coefficient and Nusselt number with respect to nanoparticles volume fraction is prominent when compared with the rate of change with variable viscosity parameter and modified Hartmann number.
The Valuation of Employees Provident Fund on Long Term Care Cost among Elderly in Malaysia
Nowadays, financing long-term care for elderly people is a crucial issue, either towards the family members or the care institution. Corresponding with the growing number of ageing population in Malaysia, there’s a need of concern on the uncertaintiness of future family care and the need for long-term care services. Moreover, with the increasing cost of living, children feels the urge of needing to work and receive a fixed monthly income that results to sending their elderly parents to care institutions. Currently, in Malaysia, the rates for private nursing homes can amount up to RM 4,000 per month excluding medical treatments and other recurring expenses. These costs are expected to be paid using their Employees Provident Fund (EPF) savings that they accumulate during their working years, especially for those working under private sectors. Hence, this study identifies the adequacy of EPF in funding the cost of long-term care service during old age. This study used a hypothetical simulation model to simulate different scenarios. The findings of this study could be used for individuals to prepare on the importance of planning for retirement, especially with the increasing cost of long-term care services.
Free Convection from a Perforated Spinning Cone with Heat Generation, Temperature-Dependent Viscosity and Partial Slip
The problem of free convection from a perforated spinning cone with viscous dissipation, temperature-dependent viscosity, and partial slip was studied. The boundary layer velocity and temperature profiles were numerically computed for different values of the spin, viscosity variation, inertia drag force, Eckert, suction/blowing parameters. The partial differential equations were transformed into a system of ordinary differential equations which were solved using the fourth-order Runge-Kutta method. This paper considered the effect of partial slip and spin parameters on the swirling velocity profiles which are rarely reported in the literature. The results obtained by this method was compared to those in the literature and found to be in agreement. Increasing the viscosity variation parameter, spin, partial slip, Eckert number, Darcian drag force parameters reduce swirling velocity profiles.
Investigating the Dynamics of Knowledge Acquisition in Learning Using Differential Equations
A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates the effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the Department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.
Computation of Reliability and Probability Weighted Moment Estimation for Three Parameter Mukherjee-Islam Failure Model
The Mukherjee-Islam Model is commonly used as a simple life time distribution to assess system reliability. The model exhibits a better fit for failure information and provides more appropriate information about hazard rate and other reliability measures as shown by various authors. We have introduced a location parameter at a time α (i.e. a time before which failure can’t occur) which makes it a more useful failure distribution than the existing ones. Even after shifting the location of the distribution, it represents a decreasing, constant and increasing failure rate. It has been shown to represent appropriate lower tail of the distribution of random variables having fixed lower bound. This study presents the reliability computations and probability weighted moment estimation of three parameter model. A comparative analysis is carried out between three parameters finite range model and some existing bathtub shaped curve fitting models. The results obtained in the study may be applied to semiconductor devices. Since probability weighted moment method is used, the results obtained can also be applied to small sample cases. Maximum likelihood estimation method is also applied in this study.
A Study of Algebraic Structure Involving Banach Space through Q-Analogue
The aim of the present paper is to study the Banach Space and Combinatorial Algebraic Structure of R. It is further aimed to study algebraic structure of set of all q-extension of classical formula and function for 0 < q < 1.
Science, Technology, Engineering And Math Approach on Playing Video Games
This STEM project is to demonstrate how to play Video Game through STEM approach and learning science and statistics. Kids are playing video games too long and parents do not want kids to play video games since most video games are not developing critical thinking. Hill Climb Car Racing game was chosen not based on commercial rating but on potential of applying statistical data-driven methodology. The author took STEM approach: Science (Physics, Mechanics), Technology (Car Upgrading), Engineering (Failure Mode), and Math (Geometry, Trigonometry and Statistics). Based on the engineering failure mode analysis and scientific understanding, author can develop a systematic car upgrading system through statistical modeling to optimize car performance. Simple linear regression was conducted to quantify the Performance Index (ROI) return (car travelling distance) of investment (car grading cost). The regression model accuracy has been improved from original 66% (random playing mode) to 92% (systematic playing mode). The ROI slope has been improved from 147.2 to 512.4 meter/upgrade unit. The clustering analysis grouped the similar field stages with common challenges and science which has helped upgrade car to support multiple stages. The best car of each stage has matched well with literature research. It’s a very successful STEM project on playing video games.
Study on a Family of Optimal Fourth-Order Multiple-Root Solver
In this paper,we develop the complex dynamics of a family of optimal fourth-order multiple-root solvers and plot their basins of attraction. Mobius conjugacy maps and extraneous fixed points applied to a prototype quadratic polynomial raised to the power of the known integer multiplicity m are investigated. A 300 x 300 uniform grid centered at the origin covering 3 x 3 square region is chosen to visualize the initial values on each basin of attraction in accordance with a coloring scheme based on their dynamical behavior. The illustrative basins of attractions applied to various test polynomials and the corresponding statistical data for convergence are shown to confirm the theoretical convergence.
A Class of Third Derivative Four-Step Exponential Fitting Numerical Integrator for Stiff Differential Equations
In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.
Modelling the Spread of HIV/AIDS Epidemic with Condom Campaign and Treatment
This paper considers a deterministic model for the transmission dynamics of HIV/AIDS in which condom campaign and treatment are both important for the disease management. In modelling of the spread of AIDS, the population is divided into six subpopulations, namely susceptible population, susceptible population who change their behavior due to education condom campaign, infected population, pre-AIDS population, treated population and full-blown AIDS population. We calculate the effective reproduction number using the next generation matrix method and investigate the existence and stability of the equilibrium points. A sensitivity analysis discovers parameters that have a high impact on effective reproduction number and should be targeted by intervention strategies. Numerical simulations are given to illustrate and verify our analytic results.
Equity Investment Restrictions and Pension Replacement Rates in Nigeria: A Ruin-Risk Analysis
Pension funds are pooled assets which are established to provide income for retirees. The funds are usually regulated to check excessive risk taking by fund managers. In Nigeria, the current defined contribution (DC) pension scheme appears to contain some overly stringent restrictions which might be hampering its successful implementation. Notable among these restrictions is the 25 percent maximum limit on investment in ordinary shares of quoted companies. This paper examines the extent to which these restrictions affect pension replacement rates at retirement. The study made use of both simulated and historical asset return distributions using mean-variance, regression analysis and ruin-risk analyses, the study found that the current equity investment restriction policy in Nigeria reduces replacement rates at retirement.
Numerical Approach to a Mathematical Modelling of Bioconvection Due to Gyrotactic Micro-Organisms over a Nonlinear Inclined Stretching Sheet Numerical Approach
The term bioconvection refers to the phenomenon of macroscopic convective motion of fluid caused by the density gradient and is created by collective swimming of motile micro-organisms. The density of base fluid increases as these self-propelled motile micro-organisms swim in a particular direction, thus causing bioconvection. It has many applications in biological systems and biotechnology. The present work represents the study of water-based nanofluid bioconvection due to gyrotactic micro-organisms over a nonlinear inclined stretching sheet. The model of the problem considers the effects of Brownian motion and thermophoresis. Boussinesq approximation is used to determine the variation of density in the buoyancy term. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformations. For computational purpose, Finite Element Method is used. The numerical results for velocity, temperature, nanoparticles concentration and density of motile micro-organism are expressed graphically. The local Skin friction coefficient, the local Nusselt number, the Sherwood number and the local density number of the motile micro-organisms are also calculated.
Analysis of Financial Time Series by Using Ornstein-Uhlenbeck Type Models
In the present work, we develop a technique for estimating the volatility of financial time series by using stochastic differential equation. Taking the daily closing prices from developed and emergent stock markets as the basis, we argue that the incorporation of stochastic volatility into the time-varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. While using the technique, we see the long-memory behavior of data sets and one-step-ahead-predicted log-volatility with 2 standard errors despite the variation of the observed noise from a Normal mixture distribution, because the financial data studied is not fully Gaussian. Also, the Ornstein-Uhlenbeck process followed in this work simulates well the financial time series, which aligns our estimation algorithm with large data sets due to the fact that this algorithm has good convergence properties.
Parallel Evaluation of Sommerfeld Integrals for Multilayer Dyadic Green's Function
Sommerfeld-integrals (SIs) are commonly encountered in electromagnetics problems involving analysis of antennas and scatterers embedded in planar multilayered media. Generally speaking, the analytical solution of SIs is unavailable, and it is well known that numerical evaluation of SIs is very time consuming and computationally expensive due to the highly oscillating and slowly decaying nature of the integrands. Therefore, fast computation of SIs has a paramount importance. In this paper, a parallel code has been developed to speed up the computation of SI in the framework of calculation of dyadic Green’s function in multilayered media. OpenMP shared memory approach is used to parallelize the SI algorithm and resulted in significant time savings. Moreover accelerating the computation of dyadic Green’s function is discussed based on the parallel SI algorithm developed.
The Volatility Forecasting in the Study of Geophysical Time Series
This work purports to study the forecasting of geophysical time series with stochastic volatility model. It has been observed that the data regarding geophysics can follow different behaviors over time, such as mean reversion and fluctuation of power spectrum. A statistical technique, which incorporates the time-varying parameters, has been proposed to analyze the seismograms of a set of earthquakes and mining explosions that occurred in the same region (within a radius of 10km). By estimating the time-varying parameters, the dynamics of the process can be fully specified, and future values can be estimated from them. Due to the heteroscedasticity, it seems appropriate to use volatility model to fit the data for studying their physical dynamic behavior. With the use of squared logarithm of observations, one-step-ahead predicted log-volatility with ± 2 standard prediction errors have been estimated despite the variation of the observed noise from a normal mixture distribution because the geophysical time series studied is not fully Gaussian. It is inferred that the incorporation of stochastic volatility into the time-varying parameter estimation significantly improves the forecasting performance, which is enacted via Maximum Likelihood Estimation. Furthermore, the estimation algorithm used in this work is compatible with large data sets, as it possesses good convergence properties.
Susceptible-Vaccinated-Infected-Recovery Model for Analyzing Tax Amnesty in Indonesia
Tax amnesty is an opportunity for a particular group of taxpayers to disclose incomplete or unreported information about previous tax periods. Tax amnesty requires specific group of taxpayers to pay certain amount relating to previous tax liability including penalties and interest without fear of criminal prosecution. This research will discuss how effective the tax amnesty using the Susceptible-Vaccinated-Infected-Recovery (SVIR) model with the population of taxpayers (S), the population in the tax amnesty program (V), the population that does not want to pay the tax (I), and the population that has revealed tax (R). The assumption used in this research is the population who does not want to pay taxes can affect people who still have responsibility to pay tax, so there is interaction between Susceptible and Infected. The tax amnesty program is a vaccine for a population of taxpayers so the population of the vaccinated taxpayers can be incorporated into population that has disclosed the tax. In addition, there is also the possibility of vaccine failure so that there is population incorporated into population that does not want to pay taxes. This SVIR model equation used differential equation system to know the effectiveness level of tax amnesty program.
Improved Elastoplastic Bounding Surface Model for the Mathematical Modeling of Geomaterials
The nature of most engineering materials is quite complex. It is, therefore, difficult to devise a general mathematical model that will simulate all possible ranges and types of excitation and behavior of a given material. As a result, the development of mathematical models is based upon simplifying assumptions regarding material behavior. Such simplifications result in some material idealization; for example, one of the simplest material idealizations is to assume that the material is elastic. However, geomaterials are nonhomogeneous, anisotropic, path-dependent materials that exhibit nonlinear stress-strain response, changes in volume under shear, dilatancy, as well as time-, rate- and temperature-dependent behavior. Over the years, many constitutive models, possessing different levels of sophistication, have been developed to simulate the behavior of geomaterials. Early in the development of constitutive models, it became evident that elastic or standard elastoplastic formulations, employing purely isotropic hardening and predicated in the existence of a yield surface surrounding a purely elastic domain, were incapable of realistically simulating the behavior of geomaterials in general, and cohesive soils in particular. Accordingly, more sophisticated constitutive models classes have been developed; one such class includes models based on the bounding surface concept. The essence of this concept is the hypothesis that inelastic deformations can occur for stress states either within or on the bounding surface. Thus, unlike classical yield surface elastoplasticity, the inelastic states are not restricted only to those lying on a surface. Elastoplastic bounding surface models have been progressively improved. Recently, the Generalized Bounding Surface Model (GBSM) for cohesive soils was been developed in an effort to conveniently unify and further improve upon past models in this class. The GBSM is a fully three-dimensional, time- and rate-dependent model that accounts for both inherent and stress induced anisotropy employing either an associative or non-associative flow rule. The GBSM includes an improved rotational hardening rule that better simulates the response of cohesive soils, particularly in extension. The GBSM is numerically implemented through a series of modular subroutines that facilitate its inclusion into new and existing research and commercial finite element computer programs. This implementation includes an adaptive multistep integration scheme in conjunction with local iteration and radial return. The one-step trapezoidal rule was used to compute the tangential stiffness matrix that defines the relationship between the stress increment and the strain increment. In verifying the predictive capabilities of the GBSM, it has been shown to successfully simulate the response of various cohesive soils, including Cardiff Kaolin, Spestone Kaolin, and Lower Cromer Till. The simulated undrained stress paths, stress-strain response, and excess pore pressures were found to be in very good agreement with the experimental values, for both compression and extension and under both drained and undrained conditions.
Spread of Measles in Indonesia with Susceptible Vaccinated Infected Recovered Model
Measles is a disease which can spread caused by a virus and has been a priority’s Ministry of Health in Indonesia to be solved. Each infected person can be recovered and get immunity so that the spread of the disease can be constructed with susceptible infected recovered (SIR). To prevent the spread of measles transmission, the Ministry of Health holds vaccinations program. The aims of the research are to derive susceptible vaccinated infected recovered (SVIR) model, to determine the patterns of disease spread with SVIR model, and also to apply the SVIR model on the spread of measles in Indonesia. Based on the article, it can be concluded that the spread model of measles with vaccinations, that is SVIR model. It is a first-order differential equation system. The patterns of disease spread is determined by solution of the model. Based on that model Indonesia will be a measles-free nation in 2186 with the average of vaccinations scope about 88% and the average score of vaccinations failure about 4.9%. If it is simulated as Ministry of Health new programs with the average of vaccinations scope about 95% and the average score of vaccinations failure about 3%, then Indonesia will be a measles-free nation in 2184. Even with the average of vaccinations scope about 100% and no failure of vaccinations, Indonesia will be a measles-free nation in 2183. Indonesia’s target as a measles-free nation in 2020 has not been reached.
Parameter Estimation of Gumbel Distribution with Maximum-Likelihood Based on Broyden Fletcher Goldfarb Shanno Quasi-Newton
Extreme data on an observation can occur due to unusual circumstances in the observation. The data can provide important information that can’t be provided by other data so that its existence needs to be further investigated. The method for obtaining extreme data is one of them using maxima block method. The distribution of extreme data sets taken with the maxima block method is called the distribution of extreme values. Distribution of extreme values is Gumbel distribution with two parameters. The parameter estimation of Gumbel distribution with maximum likelihood method (ML) is difficult to determine its exact value so that it is necessary to solve the approach. The purpose of this study was to determine the parameter estimation of Gumbel distribution with quasi-Newton BFGS method. The quasi-Newton BFGS method is a numerical method used for nonlinear function optimization without constraint so that the method can be used for parameter estimation from Gumbel distribution whose distribution function is in the form of exponential doubel function. The quasi-New BFGS method is a development of the Newton method. The Newton method uses the second derivative to calculate the parameter value changes on each iteration. Newton's method is then modified with the addition of a step length to provide a guarantee of convergence when the second derivative requires complex calculations. In the quasi-Newton BFGS method, Newton's method is modified by updating both derivatives on each iteration. The parameter estimation of the Gumbel distribution by a numerical approach using the quasi-Newton BFGS method is done by calculating the parameter values that make the distribution function maximum. In this method, we need gradient vector and hessian matrix. This research is a theory research and application by studying several journals and textbooks. The results of this study obtained the quasi-Newton BFGS algorithm and estimation of Gumbel distribution parameters. The estimation method is then applied to daily rainfall data in Purworejo District to estimate the distribution parameters. This indicates that the high rainfall that occurred in Purworejo District decreased its intensity and the range of rainfall that occurred decreased.
Nonparametric Truncated Spline Regression Model on the Data of Human Development Index in Indonesia
Human Development Index (HDI) is a standard measurement for a country's human development. Several factors may have influenced it, such as life expectancy, gross domestic product (GDP) based on the province's annual expenditure, the number of poor people, and the percentage of an illiterate people. The scatter plot between HDI and the influenced factors show that the plot does not follow a specific pattern or form. Therefore, the HDI's data in Indonesia can be applied with a nonparametric regression model. The estimation of the regression curve in the nonparametric regression model is flexible because it follows the shape of the data pattern. One of the nonparametric regression's method is a truncated spline. Truncated spline regression is one of the nonparametric approach, which is a modification of the segmented polynomial functions. The estimator of a truncated spline regression model was affected by the selection of the optimal knots point. Knot points is a focus point of spline truncated functions. The optimal knots point was determined by the minimum value of generalized cross validation (GCV). In this article were applied the data of Human Development Index with a truncated spline nonparametric regression model. The results of this research were obtained the best-truncated spline regression model to the HDI's data in Indonesia with the combination of optimal knots point 5-5-5-4. Life expectancy and the percentage of an illiterate people were the significant factors depend to the HDI in Indonesia. The coefficient of determination is 94.54%. This means the regression model is good enough to applied on the data of HDI in Indonesia.
Parameter Estimation of Additive Genetic and Unique Environment (AE) Model on Diabetes Mellitus Type 2 Using Bayesian Method
Diabetes mellitus (DM) is a chronic disease in human that occurred if pancreas cannot produce enough of insulin hormone or the body uses ineffectively insulin hormone which causes increasing level of glucose in the blood, or it was called hyperglycemia. In Indonesia, DM is a serious disease on health because it can cause blindness, kidney disease, diabetic feet (gangrene), and stroke. The type of DM criteria can also be divided based on the main causes; they are DM type 1, type 2, and gestational. Diabetes type 1 or previously known as insulin-independent diabetes is due to a lack of production of insulin hormone. Diabetes type 2 or previously known as non-insulin dependent diabetes is due to ineffective use of insulin while gestational diabetes is a hyperglycemia that found during pregnancy. The most one type commonly found in patient is DM type 2. The main factors of this disease are genetic (A) and life style (E). Those disease with 2 factors can be constructed with additive genetic and unique environment (AE) model. In this article was discussed parameter estimation of AE model using Bayesian method and the inheritance character simulation on parent-offspring. On the AE model, there are response variable, predictor variables, and parameters were capable of representing the number of population on research. The population can be measured through a taken random sample. The response and predictor variables can be determined by sample while the parameters are unknown, so it was required to estimate the parameters based on the sample. Estimation of AE model parameters was obtained based on a joint posterior distribution. The simulation was conducted to get the value of genetic variance and life style variance. The results of simulation are 0.3600 for genetic variance and 0.0899 for life style variance. Therefore, the variance of genetic factor in DM type 2 is greater than life style.
Closed-Loop Supply Chain under Price and Quality Dependent Demand: An Application to Job-Seeker Problem
The demand of a product is linearly dependent on the price and quality of the product. It is analog to the demand of the employee in job-seeker problem. This paper address a closed-loop supply chain (CLSC) where a university plays role as manufacturer that produce graduates as job-seeker according to the demand and promote them to a certain corporation through a trial. Unemployed occurs when the job-seeker failed the trial or dismissed. A third party accomodates the unemployed and sends them back to the university to increase their quality through training.
Mathematical Modeling and Analysis of Forced Vibrations in Micro-Scale Microstretch Thermoelastic Simply Supported Beam
The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler- Bernoulli beam resonators, due to exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection. The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for deflection of beam under simply supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.
Decoding and Other Symbolic Computations for the Most Important Types of Primitive Transcendental Functions
This paper develops the explicit decoding procedures for the four most important families of the Primitive Transcendental Functions. It also provides the implementation for some symbolic computations whose availability depends on the Primitive Transcendental Function type. The paper includes a partial recapitulation of definitions and fundamental properties of this vast ensemble of functions, whose euclidean vector scheme of functions representation provides important features for the symbolic computations. In fact, the paper provides the fundamental implementation specifications to facilitate the development of an efficient Computer Algebra System.
Developing and Evaluating Clinical Risk Prediction Models for Coronary Artery Bypass Graft Surgery
The ability to predict clinical outcomes is of great importance to physicians and clinicians. A number of different methods have been used in an effort to accurately predict these outcomes. These methods include the development of scoring systems based on multivariate statistical modelling, and models involving the use of classification and regression trees. The process usually consists of two consecutive phases, namely model development and external validation. The model development phase consists of building a multivariate model and evaluating its predictive performance by examining calibration and discrimination, and internal validation. External validation tests the predictive performance of a model by assessing its calibration and discrimination in different but plausibly related patients. A motivate example focuses on prediction modeling using a sample of patients undergone coronary artery bypass graft (CABG) has been used for illustrative purpose and a set of primary considerations for evaluating prediction model studies using specific quality indicators as criteria to help stakeholders evaluate the quality of a prediction model study has been proposed.
Discussion on Big Data and One of Its Early Training Application
This study focuses on a contemporary and inevitable topic of Data Science and its exemplary application for early career building: Big Data and Leaving Learning Community (LLC). ‘Academia’ and ‘Industry’ have a common sense on the importance of Big Data. However, both of them are in a threat of missing the training on this interdisciplinary area. Some traditional teaching doctrines are far away being effective on Data Science. Practitioners needs some intuition and real-life examples how to apply new methods to data in size of terabytes. We simply explain the scope of Data Science training and exemplified its early stage application with LLC, which is a National Science Foundation (NSF) founded project under the supervision of Prof. Ward since 2014. Essentially, we aim to give some intuition for professors, researchers and practitioners to combine data science tools for comprehensive real-life examples with the guides of mentees’ feedback. As a result of discussing mentoring methods and computational challenges of Big Data, we intend to underline its potential with some more realization.
An Information-Based Approach for Preference Method in Multi-Attribute Decision Making
Multi-Criteria Decision Making (MCDM) is the modelling of real-life to solve problems we encounter. It is a discipline that aids decision makers who are faced with conflicting alternatives to make an optimal decision. MCDM problems can be classified into two main categories: Multi-Attribute Decision Making (MADM) and Multi-Objective Decision Making (MODM), based on the different purposes and different data types. Although various MADM techniques were developed for the problems encountered, their methodology is limited in modelling real-life. Moreover, objective results are hard to obtain, and the findings are generally derived from subjective data. Although, new and modified techniques are developed by presenting new approaches such as fuzzy logic; comprehensive techniques, even though they are better in modelling real-life, could not find a place in real world applications for being hard to apply due to its complex structure. These constraints restrict the development of MADM. This study aims to conduct a comprehensive analysis of preference methods in MADM and propose an approach based on information. For this purpose, a detailed literature review has been conducted, current approaches with their advantages and disadvantages have been analyzed. Then, the approach has been introduced. In this approach, performance values of the criteria are calculated in two steps: first by determining the distribution of each attribute and standardizing them, then calculating the information of each attribute as informational energy.
A Family of Second Derivative Methods for Numerical Integration of Stiff Initial Value Problems in Ordinary Differential Equations
Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.
Convergence Analysis of Cubic B-Spline Collocation Method for Time Dependent Parabolic Advection-Diffusion Equations
A comprehensive numerical study is presented for the solution of time-dependent advection diffusion problems by using cubic B-spline collocation method. The linear combination of cubic B-spline basis, taken as approximating function, is evaluated using the zeros of shifted Chebyshev polynomials as collocation points in each element to obtain the best approximation. A comparison, on the basis of efficiency and accuracy, with the previous techniques is made which confirms the superiority of the proposed method. An asymptotic convergence analysis of technique is also discussed, and the method is found to be of order two. The theoretical analysis is supported with suitable examples to show second order convergence of technique. Different numerical examples are simulated using MATLAB in which the 3-D graphical presentation has taken at different time steps as well as different domain of interest.
A Method for Solving Bi-Objective Transportation Problem under Fuzzy Environment
A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than others existing algorithms for the given uncertain transportation problem.