Search results for: mathematical equations

Authors: Hsueh-Cheng Yang

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The generation and design of compound involute spur gearings can be used in gear pump. A compound rack cutter with asymmetric involute teeth is presented for determining the mathematical model of compound gear pumps. This paper covers the following topics: (a) generation and geometry of compound rack cutter is presented and used to generate a compound gear and a compound pinion. (b) Based on the developed compound gears, stress analysis was performed for the symmetric gears and the asymmetric gears. Comparing the results of the stress analysis for the asymmetric involute teeth is superior to the symmetric involute teeth. A numerical example that illustrates the developed compound rack cutter is represented.

Keywords: compound, involute teeth, gear pump, rack cutter

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Cristian Pauna

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With few steps away from the 2020, investments in financial markets is a common activity nowadays. In the electronic trading environment, the automated investment software has become a major part in the business intelligence system of any modern financial company. The investment decisions are assisted and/or made automatically by computers using mathematical algorithms today. The complexity of these algorithms requires computer assistance in the investment process. This paper will present several investment strategies that can be automated with algorithmic trading for Deutscher Aktienindex DAX30. It was found that, based on several price action mathematical models used for high-frequency trading some investment strategies can be optimized and improved for automated investments with good results. This paper will present the way to automate these investment decisions. Automated signals will be built using all of these strategies. Three major types of investment strategies were found in this study. The types are separated by the target length and by the exit strategy used. The exit decisions will be also automated and the paper will present the specificity for each investment type. A comparative study will be also included in this paper in order to reveal the differences between strategies. Based on these results, the profit and the capital exposure will be compared and analyzed in order to qualify the investment methodologies presented and to compare them with any other investment system. As conclusion, some major investment strategies will be revealed and compared in order to be considered for inclusion in any automated investment system.

Keywords: Algorithmic trading, automated investment systems, limit conditions, trading principles, trading strategies

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Authors: Gareth Baxter

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We use a mathematical model of language change to examine two recently observed patterns of language change: one in which most speakers change gradually, following the mean of the community change, and one in which most individuals use predominantly one variant or another, and change rapidly if they change at all. The model is based on Croft’s Utterance Selection account of language change, which views language change as an evolutionary process, in which different variants (different ‘ways of saying the same thing’) compete for usage in a population of speakers. Language change occurs when a new variant replaces an older one as the convention within a given population. The present model extends a previous simpler model to include effects related to speaker aging and interspeaker variation in behaviour. The two patterns of individual change (one more centralized and the other more polarized) were recently observed in historical language changes, and it was further observed that slower changes were more associated with the centralized pattern, while quicker changes were more polarized. Our model suggests that the two patterns of change can be explained by different balances between the preference of speakers to use one variant over another and the degree of accommodation to (propensity to adapt towards) other speakers. The correlation with the rate of change appears naturally in our model, and results from the fact that both differential weighting of variants and the degree of accommodation affect the time for change to occur, while also determining the patterns of change. This work represents part of an ongoing effort to examine phenomena in language change through the use of mathematical models. This offers another way to evaluate qualitative explanations that cannot be practically tested (or cannot be tested at all) in a real-world, large-scale speech community.

Keywords: agent based modeling, cultural evolution, language change, social behavior modeling, social influence

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Authors: M. Cardenas-Garcia, P. P. Gonzalez-Perez

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Intercellular communication is a necessary condition for cellular functions and it allows a group of cells to survive as a population. Throughout this interaction, the cells work in a coordinated and collaborative way which facilitates their survival. In the case of cancerous cells, these take advantage of intercellular communication to preserve their malignancy, since through these physical unions they can send signs of malignancy. The Wnt/β-catenin signaling pathway plays an important role in the formation of intercellular communications, being also involved in a large number of cellular processes such as proliferation, differentiation, adhesion, cell survival, and cell death. The modeling and simulation of cellular signaling systems have found valuable support in a wide range of modeling approaches, which cover a wide spectrum ranging from mathematical models; e.g., ordinary differential equations, statistical methods, and numerical methods– to computational models; e.g., process algebra for modeling behavior and variation in molecular systems. Based on these models, different simulation tools have been developed from mathematical ones to computational ones. Regarding cellular and molecular processes in cancer, its study has also found a valuable support in different simulation tools that, covering a spectrum as mentioned above, have allowed the in silico experimentation of this phenomenon at the cellular and molecular level. In this work, we simulate and explore the complex interaction patterns of intercellular communication in cancer cells using the Cellulat bioinformatics tool, a computational simulation tool developed by us and motivated by two key elements: 1) a biochemically inspired model of self-organizing coordination in tuple spaces, and 2) the Gillespie’s algorithm, a stochastic simulation algorithm typically used to mimic systems of chemical/biochemical reactions in an efficient and accurate way. The main idea behind the Cellulat simulation tool is to provide an in silico experimentation environment that complements and guides in vitro experimentation in intra and intercellular signaling networks. Unlike most of the cell signaling simulation tools, such as E-Cell, BetaWB and Cell Illustrator which provides abstractions to model only intracellular behavior, Cellulat is appropriate for modeling both intracellular signaling and intercellular communication, providing the abstractions required to model –and as a result, simulate– the interaction mechanisms that involve two or more cells, that is essential in the scenario discussed in this work. During the development of this work we made evident the application of our computational simulation tool (Cellulat) for the modeling and simulation of intercellular communication between normal and cancerous cells, and in this way, propose key molecules that may prevent the arrival of malignant signals to the cells that surround the tumor cells. In this manner, we could identify the significant role that has the Wnt/β-catenin signaling pathway in cellular communication, and therefore, in the dissemination of cancer cells. We verified, using in silico experiments, how the inhibition of this signaling pathway prevents that the cells that surround a cancerous cell are transformed.

Keywords: cancer cells, in silico approach, intercellular communication, key molecules, modeling and simulation

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Authors: Evln Ranga Charyulu, S. P. Venu Madhavarao, S. Udaya kumar, S. V. S. S. N. V. G. Krishna Murthy

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With the advent of new nanometer process technologies, it is possible to integrate billion transistors on a single substrate. When more and more functionality included there is the possibility of multi-million transistors switching simultaneously consuming more power and dissipating more power along with more leakage of current into the substrate of porous silicon or germanium material. These results in substrate heating and thermal noise generation coupled to signals of interest. The heating process is represented by coupled nonlinear partial differential equations in porous silicon and germanium. By identifying heat sources and heat fluxes may results in designing of ultra-low power circuits. The PDEs are solved by finite difference scheme assuming that boundary layer equations in porous silicon and germanium. Local heat fluxes along the vertical isothermal surface immersed in porous SI/Ge are considered. The parameters considered for optimization are thermal diffusivity, thermal expansion coefficient, thermal diffusion ratio, permeability, specific heat at constant temperatures, Rayleigh number, amplitude of wavy surface, mass expansion coefficient. The diffusion of heat was caused by the concentration gradient. Thermal physical properties are homogeneous and isotropic. By using L8, TAGUCHI method the parameters are optimized.

Keywords: heat transfer, pde, taguchi optimization, SI/Ge

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Authors: Fahad Suleiman

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Agriculture has been the mainstay of the nation’s economy in Nigeria. It provides food for the ever rapidly increasing population and raw materials for the industries. People especially the rural dwellers are gainfully employed on their crop farms and small-scale livestock farms for income earning. In farming, availability of funds and time management are one of the major factors that influence the system of farming in Nigeria in which mathematical science knowledge was highly required in order for farms to be managed effectively. Farmers often applied mathematics, almost every day for a variety of tasks, ranging from measuring and weighing, to land marking. This paper, therefore, explores some of the ways math is used in farming. For instance, farmers use arithmetic variety of farm activities such as seed planting, harvesting crop, cultivation and mulching. It is also important in helping farmers to know how much their livestock weighs, how much milk their cows produce and crop yield per acres, among others.

Keywords: agriculture, application, economic, farming, mathematics

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Authors: Dana Kristalova

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This article deals with geographical conditions in terrain and their effect on the movement of vehicles, their effect on speed and safety of movement of people and vehicles. Finding of the optimal routes outside the communication is studied in the army environment, but it occur in civilian as well, primarily in crisis situation, or by the provision of assistance when natural disasters such as floods, fires, storms, etc. have happened. These movements require the optimization of routes when effects of geographical factors should be included. The most important factor is surface of the terrain. It is based on several geographical factors as are slopes, soil conditions, micro-relief, a type of surface and meteorological conditions. Their mutual impact has been given by coefficient of deceleration. This coefficient can be used for commander´s decision. New approaches and methods of terrain testing, mathematical computing, mathematical statistics or cartometric investigation are necessary parts of this evaluation.

Keywords: surface of a terrain, movement of vehicles, geographical factor, optimization of routes

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Authors: Filipe Cardoso de Oliveira, Lino Marcos da Silva, Ademar Nogueira do Nascimento, Cristiano Hora de Oliveira Fontes

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This article presents a mathematical formulation for the production Break-Even Point problem in a non-homogeneous system. The optimization problem aims to obtain the composition of the best product mix in a non-homogeneous industrial plant, with the lowest cost until the breakeven point is reached. The problem constraints represent real limitations of a generic non-homogeneous industrial plant for n different products. The proposed model is able to solve the equilibrium point problem simultaneously for all products, unlike the existing approaches that propose a resolution in a sequential way, considering each product in isolation and providing a sub-optimal solution to the problem. The results indicate that the product mix found through the proposed model has economical advantages over the traditional approach used.

Keywords: branch and bound, break-even point, non-homogeneous production system, integer linear programming, management accounting

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Authors: Ibrahim Yakubu Seini, Oluwole Daniel Makinde

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MHD chemically reacting viscous fluid flow towards a vertical surface with slip and convective boundary conditions has been conducted. The temperature and the chemical species concentration of the surface and the velocity of the external flow are assumed to vary linearly with the distance from the vertical surface. The governing differential equations are modeled and transformed into systems of ordinary differential equations, which are then solved numerically by a shooting method. The effects of various parameters on the heat and mass transfer characteristics are discussed. Graphical results are presented for the velocity, temperature, and concentration profiles whilst the skin-friction coefficient and the rate of heat and mass transfers near the surface are presented in tables and discussed. The results revealed that increasing the strength of the magnetic field increases the skin-friction coefficient and the rate of heat and mass transfers toward the surface. The velocity profiles are increased towards the surface due to the presence of the Lorenz force, which attracts the fluid particles near the surface. The rate of chemical reaction is seen to decrease the concentration boundary layer near the surface due to the destructive chemical reaction occurring near the surface.

Keywords: boundary layer, surface slip, MHD flow, chemical reaction, heat transfer, mass transfer

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Authors: Gholamhassan Kakha, Mohsen Jami, Daniel Alex Merino Natorce

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Sustainable development refers to the creation of a balance between the development and the environment too; it consists of three key principles namely environment, society and economy. These three parameters are related to each other and the imbalance occurs in each will lead to the disparity of the other parts. Mining is one of the most important tools of the economic growth and social welfare in many countries. Meanwhile, assessment of the environmental impacts has directed to the attention of planners toward the natural environment of the areas surrounded by mines and allowing for monitoring and controlling of the current situation by the designers. In this look upon, a semi-quantitative model using a matrix method is presented for assessing the environmental impacts in the BOOG Granite Mine located in Sistan and Balouchestan, one of the provinces of Iran for determining the effective factors and environmental components. For accomplishing this purpose, the initial data are collected by the experts at the next stage; the effect of the factors affects each environmental component is determined by specifying the qualitative viewpoints. Based on the results, factors including air quality, ecology, human health and safety along with the environmental damages resulted from mining activities in that area. Finally, the results gained from the assessment of the environmental impact are used to evaluate the sustainability by using Philips mathematical model. The results show that the sustainability of this area is weak, so environmental preventive measures are recommended to reduce the environmental damages to its components.

Keywords: sustainable development, environmental impacts' assessment, BOOG granite, Philips mathematical model

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Authors: M. Isabel Santos, Ana Breda, Ana Margarida Almeida

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Research on academic abilities of individuals with autism spectrum disorder (ASD) underlines the importance of mathematics interventions. Yet the proposal of digital applications for children and youth with ASD continues to attract little attention, namely, regarding the development of mathematical reasoning, being the use of the digital technologies an area of great interest for individuals with this disorder and its use is certainly a facilitative strategy in the development of their mathematical abilities. The use of digital technologies can be an effective way to create innovative learning opportunities to these students and to develop creative, personalized and constructive environments, where they can develop differentiated abilities. The children with ASD often respond well to learning activities involving information presented visually. In this context, we present the digital Learning Environment on Mathematics for Autistic children (LEMA) that was a research project conducive to a PhD in Multimedia in Education and was developed by the Thematic Line Geometrix, located in the Department of Mathematics, in a collaboration effort with DigiMedia Research Center, of the Department of Communication and Art (University of Aveiro, Portugal). LEMA is a digital mathematical learning environment which activities are dynamically adapted to the user’s profile, towards the development of mathematical abilities of children aged 6–12 years diagnosed with ASD. LEMA has already been evaluated with end-users (both students and teacher’s experts) and based on the analysis of the collected data readjustments were made, enabling the continuous improvement of the prototype, namely considering the integration of universal design for learning (UDL) approaches, which are of most importance in ASD, due to its heterogeneity. The learning strategies incorporated in LEMA are: (i) provide options to custom choice of math activities, according to user’s profile; (ii) integrates simple interfaces with few elements, presenting only the features and content needed for the ongoing task; (iii) uses a simple visual and textual language; (iv) uses of different types of feedbacks (auditory, visual, positive/negative reinforcement, hints with helpful instructions including math concept definitions, solved math activities using split and easier tasks and, finally, the use of videos/animations that show a solution to the proposed activity); (v) provides information in multiple representation, such as text, video, audio and image for better content and vocabulary understanding in order to stimulate, motivate and engage users to mathematical learning, also helping users to focus on content; (vi) avoids using elements that distract or interfere with focus and attention; (vii) provides clear instructions and orientation about tasks to ease the user understanding of the content and the content language, in order to stimulate, motivate and engage the user; and (viii) uses buttons, familiarly icons and contrast between font and background. Since these children may experience little sensory tolerance and may have an impaired motor skill, besides the user to have the possibility to interact with LEMA through the mouse (point and click with a single button), the user has the possibility to interact with LEMA through Kinect device (using simple gesture moves).

Keywords: autism spectrum disorder, digital technologies, inclusion, mathematical abilities, mathematical learning activities

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Authors: Ridha Fethi Mechlouch, Ahlem Ayadi, Ammar Ben Brahim

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Given the importance of the preservation of polyphenols and carotenoids during thermal processing, we attempted in this study to investigate the variation of these two parameters in faba beans during microwave treatment using different power densities (1; 2; and 3W/g), then to perform a mathematical modeling by using non-linear regression analysis to evaluate the models constants. The variation of the carotenoids and polyphenols ratio of faba beans and the models are tested to validate the experimental results. Exponential models were found to be suitable to describe the variation of caratenoid ratio (R²= 0.945, 0.927 and 0.946) for power densities (1; 2; and 3W/g) respectively, and polyphenol ratio (R²= 0.931, 0.989 and 0.982) for power densities (1; 2; and 3W/g) respectively. The effect of microwave power density Pd(W/g) on the coefficient k of models were also investigated. The coefficient is highly correlated (R² = 1) and can be expressed as a polynomial function.

Keywords: microwave treatment, power density, carotenoid, polyphenol, modeling

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Authors: Nurul Liyana Abdul Aziz, Nur Aidya Hanum Aizam

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Course timetabling problems occur every semester in a university which includes the allocation of resources (subjects, lecturers and students) to a number of fixed rooms and timeslots. The assignment is carried out in a way such that there are no conflicts within rooms, students and lecturers, as well as fulfilling a range of constraints. The constraints consist of rules and policies set up by the universities as well as lecturers’ and students’ preferences of courses to be allocated in specific timeslots. This paper specifically focuses on the preferences of the course timetabling problem in one of the public universities in Malaysia. The demands will be considered into our existing mathematical model to make it more generalized and can be used widely. We have distributed questionnaires to a number of lecturers and students of the university to investigate their demands and preferences for their desired course timetable. We classify the preferences thus converting them to construct one mathematical model that can produce such timetable.

Keywords: university course timetabling problem, integer programming, preferences, constraints

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Authors: Vijay Kr. Yadav, Nilam Rathi

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Accurate prediction of glucose level for diabetes mellitus is required to avoid affecting the functioning of major organs of human body. This study describes the fundamental assumptions and two different methodologies of the Blood glucose prediction. First is based on the back-propagation algorithm of Artificial Neural Network (ANN), and second is based on the Neuro-Fuzzy technique, called Fuzzy Inference System (FIS). Errors between proposed methods further discussed through various statistical methods such as mean square error (MSE), normalised mean absolute error (NMAE). The main objective of present study is to develop mathematical model for blood glucose prediction before 12 hours advanced using data set of three patients for 60 days. The comparative studies of the accuracy with other existing models are also made with same data set.

Keywords: back-propagation, diabetes mellitus, fuzzy inference system, neuro-fuzzy

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Authors: Ranjith Maniyeri, Ahamed C. Saleel

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Two-dimensional fluid flow over a stationary circular cylinder is one of the bench mark problem in the field of fluid-structure interaction in computational fluid dynamics (CFD). Motivated by this, in the present work, a two-dimensional computational model is developed using an improved version of immersed boundary method which combines the feedback forcing scheme of the virtual boundary method with Peskin’s regularized delta function approach. Lagrangian coordinates are used to represent the cylinder and Eulerian coordinates are used to describe the fluid flow. A two-dimensional Dirac delta function is used to transfer the quantities between the sold to fluid domain. Further, continuity and momentum equations governing the fluid flow are solved using fractional step based finite volume method on a staggered Cartesian grid system. The developed code is validated by comparing the values of drag coefficient obtained for different Reynolds numbers with that of other researcher’s results. Also, through numerical simulations for different Reynolds numbers flow behavior is well captured. The stability analysis of the improved version of immersed boundary method is tested for different values of feedback forcing coefficients.

Keywords: Feedback Forcing Scheme, Finite Volume Method, Immersed Boundary Method, Navier-Stokes Equations

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Authors: Santhosh Srinivasan, Vipul Garhiya, Shahul Hamid Khan

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Environmental performance along with social performance is becoming vital factors for industries to achieve global standards. With a good environmental policy global industries are differentiating them from their competitors. This paper concentrates on multi stage, multi product and multi period manufacturing network. Single objective mathematical models for a total cost for the entire forward supply chain and reverse chain are considered. Here five different problems are considered by varying the number of facilities for illustration. M-MOGA, Shuffle Frog Leaping algorithm (SFLA) and CPLEX are used for finding the optimal solution for the mathematical model.

Keywords: closed loop supply chain, genetic algorithm, random search, multi period, green supply chain

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Authors: H. Ozbasaran

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Lateral torsional buckling is a global stability loss which should be considered in the design of slender structural members under flexure about their strong axis. It is possible to compute the load which causes lateral torsional buckling of a beam by finite element analysis, however, closed form equations are needed in engineering practice. Such equations can be obtained by using energy method. Unfortunately, this method has a vital drawback. In lateral torsional buckling applications of energy method, a proper function for the critical lateral torsional buckling mode should be chosen which can be thought as the variation of twisting angle along the buckled beam. The accuracy of the results depends on how close is the chosen function to the exact mode. Since critical lateral torsional buckling mode of the cantilever I-beams varies due to material properties, section properties, and loading case, the hardest step is to determine a proper mode function. This paper presents an approximate function for critical lateral torsional buckling mode of doubly symmetric cantilever I-beams. Coefficient matrices are calculated for the concentrated load at the free end, uniformly distributed load and constant moment along the beam cases. Critical lateral torsional buckling modes obtained by presented function and exact solutions are compared. It is found that the modes obtained by presented function coincide with differential equation solutions for considered loading cases.

Keywords: buckling mode, cantilever, lateral-torsional buckling, I-beam

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Authors: Susmita Panda, Arnab Banerjee, Ajinkya Baxy, Bappaditya Manna

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The design of short to medium-span high-speed bridges in critical locations is an essential aspect of vehicle-bridge interaction. Due to dynamic interaction between moving load and bridge, mathematical models or finite element modeling computations become time-consuming. Thus, to reduce the computational effort, a universal approximator using an artificial neural network (ANN) has been used to evaluate the dynamic response of the bridge. The data set generation and training of surrogate models have been conducted over the results obtained from mathematical modeling. Further, the robustness of the surrogate model has been investigated, which showed an error percentage of less than 10% with conventional methods. Additionally, the dependency of the dynamic response of the bridge on various load and bridge parameters has been highlighted through a parametric study.

Keywords: artificial neural network, mode superposition method, moving load analysis, surrogate models

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Authors: P. G. Siddheshwar, R. K. Vanishree, C. Kanchana

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A local nonlinear stability analysis using a eight-mode expansion is performed in arriving at the coupled amplitude equations for Rayleigh-Bénard-Brinkman convection (RBBC) in the presence of LTNE effects. Streamlines and isotherms are obtained in the two-dimensional unsteady finite-amplitude convection regime. The parameters’ influence on heat transport is found to be more pronounced at small time than at long times. Results of the Rayleigh-Bénard convection is obtained as a particular case of the present study. Additional modes are shown not to significantly influence the heat transport thus leading us to infer that five minimal modes are sufficient to make a study of RBBC. The present problem that uses rolls as a pattern of manifestation of instability is a needed first step in the direction of making a very general non-local study of two-dimensional unsteady convection. The results may be useful in determining the preferred range of parameters’ values while making rheometric measurements in fluids to ascertain fluid properties such as viscosity. The results of LTE are obtained as a limiting case of the results of LTNE obtained in the paper.

Keywords: coupled Ginzburg–Landau model, local thermal non-equilibrium (LTNE), local thermal equilibrium (LTE), Rayleigh–Bénard-Brinkman convection

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Authors: Judith Stein, Elfriede Friedmann

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The injection of a drug into the vitreous body for the treatment of retinal diseases like wet aged-related macular degeneration (AMD) is the most common medical intervention worldwide. We develop mathematical models for drug transport in the vitreous body of a human eye to analyse the impact of different rheological models of the vitreous on drug distribution. In addition to the convection diffusion equation characterizing the drug spreading, we use porous media modeling for the healthy vitreous with a dense collagen network and include the steady permeating flow of the aqueous humor described by Darcy's law driven by a pressure drop. Additionally, the vitreous body in a healthy human eye behaves like a viscoelastic gel through the collagen fibers suspended in the network of hyaluronic acid and acts as a drug depot for the treatment of retinal diseases. In a completely liquefied vitreous, we couple the drug diffusion with the classical Navier-Stokes flow equations. We prove the global existence and uniqueness of the weak solution of the developed initial-boundary value problem describing the drug distribution in the healthy vitreous considering the permeating aqueous humor flow in the realistic three-dimensional setting. In particular, for the drug diffusion equation, results from the literature are extended from homogeneous Dirichlet boundary conditions to our mixed boundary conditions that describe the eye with the Galerkin's method using Cauchy-Schwarz inequality and trace theorem. Because there is only a small effective drug concentration range and higher concentrations may be toxic, the ability to model the drug transport could improve the therapy by considering patient individual differences and give a better understanding of the physiological and pathological processes in the vitreous.

Keywords: coupled PDE systems, drug diffusion, mixed boundary conditions, vitreous body

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Authors: Carlos A. Vega-Posada, Jeisson Alejandro Higuita-Villa, Julio C. Saldarriaga-Molina

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This paper presents a simplified analytical approach to conduct elastic stability and second-order lateral stiffness analyses of beam-column elements (i.e., piles) with generalized end-boundary conditions embedded on a homogeneous or non-homogeneous Pasternak foundation. The solution is derived using the well-known Differential Transformation Method (DTM), and it consists simply of solving a system of two linear algebraic equations. Using other conventional approaches to solve the governing differential equation of the proposed element can be cumbersome and the solution challenging to implement, especially when the non-homogeneity of the soil is considered. The proposed formulation includes the effects of i) any rotational or lateral transverse spring at the ends of the pile, ii) any external transverse load acting along the pile, iii) soil non-homogeneity, and iv) the second-parameter of the elastic foundation (i.e., shear layer connecting the springs at the top). A parametric study is conducted to investigate the effects of different modulus of subgrade reactions, degrees of non-homogeneities, and intermediate end-boundary conditions on the pile response. The same set of equations can be used to conduct both elastic stability and static analyses. Comprehensive examples are presented to show the simplicity and practicability of the proposed method.

Keywords: elastic stability, second-order lateral stiffness, soil-non-homogeneity, pile analysis

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Authors: Nader Al-Rashidi, David Greenhalgh

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Mathematical modelling techniques are now being used by health organizations worldwide to help understand the likely impact that intervention strategies treatment options and combinations of these have on the prevalence and incidence of hepatitis C virus (HCV) in the people who inject drugs (PWID) population. In this poster, we develop a deterministic, compartmental mathematical model to approximate the spread of the HCV in a PWID population that has been divided into two groups by time since onset of injection. The model assumes that after injection needles adopt the most infectious state of their previous state or that of the PWID who last injected with them. Using analytical techniques, we find that the model behaviour is determined by the basic reproductive number R₀, where R₀ = 1 is a critical threshold separating two different outcomes. The disease-free equilibrium is globally stable if R₀ ≤ 1 and unstable if R₀ > 1. Additionally, we make some simulations where have confirmed that the model tends to this endemic equilibrium value with realistic parameter values giving an HCV prevalence.

Keywords: hepatitis C, people who inject drugs, HCV, PWID

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Authors: Sumeyra Karatas, Veysel Karatas, Reyhan Safak, Gamze Bulut-Ozturk, Ozgul Kartal

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Productive struggle entails a student's cognitive exertion to comprehend mathematical concepts and uncover solutions not immediately apparent. The significance of productive struggle in learning mathematics is accentuated by influential educational theorists, emphasizing its necessity for learning mathematics with understanding. Consequently, supporting productive struggle in learning mathematics is recognized as a high-leverage and effective mathematics teaching practice. In this study, the investigation into the role of productive struggle in learning mathematics led to the development of a comprehensive rubric for productive struggle pedagogy through an exhaustive literature review. The rubric consists of eight primary criteria and 37 sub-criteria, providing a detailed description of teacher actions and pedagogical choices that foster students' productive struggles. These criteria encompass various pedagogical aspects, including task design, tool implementation, allowing time for struggle, posing questions, scaffolding, handling mistakes, acknowledging efforts, and facilitating discussion/feedback. Utilizing this rubric, a team of researchers and teachers designed eight 90-minute lesson plans, employing a productive struggle pedagogy, for a two-week unit on solving systems of linear equations. Simultaneously, another set of eight lesson plans on the same topic, featuring identical content and problems but employing a traditional lecture-and-practice model, was designed by the same team. The objective was to assess the impact of supporting productive struggle on students' mathematics learning, defined by the strands of mathematical proficiency. This quasi-experimental study compares the control group, which received traditional lecture- and practice instruction, with the treatment group, which experienced a productive struggle in pedagogy. Sixty-six 10th and 11th-grade students from two algebra classes, taught by the same teacher at a high school, underwent either the productive struggle pedagogy or lecture-and-practice approach over two-week eight 90-minute class sessions. To measure students' learning, an assessment was created and validated by a team of researchers and teachers. It comprised seven open-response problems assessing the strands of mathematical proficiency: procedural and conceptual understanding, strategic competence, and adaptive reasoning on the topic. The test was administered at the beginning and end of the two weeks as pre-and post-test. Students' solutions underwent scoring using an established rubric, subjected to expert validation and an inter-rater reliability process involving multiple criteria for each problem based on their steps and procedures. An analysis of covariance (ANCOVA) was conducted to examine the differences between the control group, which received traditional pedagogy, and the treatment group, exposed to the productive struggle pedagogy, on the post-test scores while controlling for the pre-test. The results indicated a significant effect of treatment on post-test scores for procedural understanding (F(2, 63) = 10.47, p < .001), strategic competence (F(2, 63) = 9.92, p < .001), adaptive reasoning (F(2, 63) = 10.69, p < .001), and conceptual understanding (F(2, 63) = 10.06, p < .001), controlling for pre-test scores. This demonstrates the positive impact of supporting productive struggle in learning mathematics. In conclusion, the results revealed the significance of the role of productive struggle in learning mathematics. The study further explored the practical application of productive struggle through the development of a comprehensive rubric describing the pedagogy of supporting productive struggle.

Keywords: effective mathematics teaching practice, high school algebra, learning mathematics, productive struggle

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Authors: Hamsini Pulugurtha, V.S. Lakshmi Jagadmaba Paluri

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Distributed denial of service attack (DDoS) is one altogether the top-rated cyber threats presently. It runs down the victim server resources like a system of measurement and buffer size by obstructing the server to supply resources to legitimate shoppers. Throughout this text, we tend to tend to propose a mathematical model of DDoS attack; we discuss its relevancy to the choices like inter-arrival time or rate of arrival of the assault customers accessing the server. We tend to tend to further analyze the attack model in context to the exhausting system of measurement and buffer size of the victim server. The projected technique uses an associate in nursing unattended learning technique, self-organizing map, to make the clusters of identical choices. Lastly, the abstract applies mathematical correlation and so the standard likelihood distribution on the clusters and analyses their behaviors to look at a DDoS attack. These systems not exclusively interconnect very little devices exchanging personal data, but to boot essential infrastructures news standing of nuclear facilities. Although this interconnection brings many edges and blessings, it to boot creates new vulnerabilities and threats which might be conversant in mount attacks. In such sophisticated interconnected systems, the power to look at attacks as early as accomplishable is of paramount importance.

Keywords: application attack, bandwidth, buffer correlation, DDoS distribution flooding intrusion layer, normal prevention probability size

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Deva Kanta Phukan

Abstract:

An investigation is made to carry out to study the thermal-diffusion and diffusion thermo-effects in hydro-magnetic unsteady flow by a mixed convection boundary layer past an impermeable vertical stretching sheet embedded in a conducting fluid-saturated porous medium in the presence of a chemical reaction effect. The velocity of stretching surface, the surface temperature and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed in to self similar unsteady equations using similarity transformations and solved numerically by the Runge kutta fourth order scheme in association with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, temperature, the concentration, the skin friction , and the Nusselt and Sherwood numbers are shown graphically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.

Keywords: heat and mass transfer, boundary layer flow, porous media, magnetic field, Soret number, Dufour’s number

Procedia PDF Downloads 445

Authors: Yung C. Lin, Kung D. Wu, Wei C. Shih, Jui P. Hung

Abstract:

High speed and high precision machining have become the most important technology in manufacturing industry. The surface roughness of high precision components is regarded as the important characteristics of the product quality. However, machining chatter could damage the machined surface and restricts the process efficiency. Therefore, selection of the appropriate cutting conditions is of importance to prevent the occurrence of chatter. In addition, vibration of the spindle tool also affects the surface quality, which implies the surface precision can be controlled by monitoring the vibration of the spindle tool. Based on this concept, this study was aimed to investigate the influence of the machining conditions on the surface roughness and the vibration of the spindle tool. To this end, a series of machining tests were conducted on aluminum alloy. In tests, the vibration of the spindle tool was measured by using the acceleration sensors. The surface roughness of the machined parts was examined using white light interferometer. The response surface methodology (RSM) was employed to establish the mathematical models for predicting surface finish and tool vibration, respectively. The correlation between the surface roughness and spindle tool vibration was also analyzed by ANOVA analysis. According to the machining tests, machined surface with or without chattering was marked on the lobes diagram as the verification of the machining conditions. Using multivariable regression analysis, the mathematical models for predicting the surface roughness and tool vibrations were developed based on the machining parameters, cutting depth (a), feed rate (f) and spindle speed (s). The predicted roughness is shown to agree well with the measured roughness, an average percentage of errors of 10%. The average percentage of errors of the tool vibrations between the measurements and the predictions of mathematical model is about 7.39%. In addition, the tool vibration under various machining conditions has been found to have a positive influence on the surface roughness (r=0.78). As a conclusion from current results, the mathematical models were successfully developed for the predictions of the surface roughness and vibration level of the spindle tool under different cutting condition, which can help to select appropriate cutting parameters and to monitor the machining conditions to achieve high surface quality in milling operation.

Keywords: machining parameters, machining stability, regression analysis, surface roughness

Procedia PDF Downloads 231

Authors: Y. Sunecher, N. Mamode Khan, V. Jowaheer

Abstract:

This paper considers the modelling of a non-stationary bivariate integer-valued autoregressive moving average of order one (BINARMA(1,1)) with correlated Poisson innovations. The BINARMA(1,1) model is specified using the binomial thinning operator and by assuming that the cross-correlation between the two series is induced by the innovation terms only. Based on these assumptions, the non-stationary marginal and joint moments of the BINARMA(1,1) are derived iteratively by using some initial stationary moments. As regards to the estimation of parameters of the proposed model, the conditional maximum likelihood (CML) estimation method is derived based on thinning and convolution properties. The forecasting equations of the BINARMA(1,1) model are also derived. A simulation study is also proposed where BINARMA(1,1) count data are generated using a multivariate Poisson R code for the innovation terms. The performance of the BINARMA(1,1) model is then assessed through a simulation experiment and the mean estimates of the model parameters obtained are all efficient, based on their standard errors. The proposed model is then used to analyse a real-life accident data on the motorway in Mauritius, based on some covariates: policemen, daily patrol, speed cameras, traffic lights and roundabouts. The BINARMA(1,1) model is applied on the accident data and the CML estimates clearly indicate a significant impact of the covariates on the number of accidents on the motorway in Mauritius. The forecasting equations also provide reliable one-step ahead forecasts.

Keywords: non-stationary, BINARMA(1, 1) model, Poisson innovations, conditional maximum likelihood, CML

Procedia PDF Downloads 129

Authors: Nazli Uren, Ayse Okur

Abstract:

Tactile comfort of a textile product is an essential property and a major concern when it comes to customer perceptions and preferences. The subjective nature of comfort and the difficulties regarding the simulation of human hand sensory feelings make it hard to establish a well-accepted link between tactile comfort and objective evaluations. On the other hand, shear behavior of a fabric is a mechanical parameter which can be measured by various objective test methods. The principal aim of this study is to determine the tactile comfort of commercially available denim fabrics by subjective measurements, create a tactile score database for denim fabrics and investigate the relations between tactile comfort and shear behavior. In-plane shear behaviors of 17 different commercially available denim fabrics with a variety of raw material and weave structure were measured by a custom design shear frame and conventional bias extension method in two corresponding diagonal directions. Tactile comfort of denim fabrics was determined via subjective customer evaluations as well. Aforesaid relations were statistically investigated and introduced as regression equations. The analyses regarding the relations between tactile comfort and shear behavior showed that there are considerably high correlation coefficients. The suggested regression equations were likewise found out to be statistically significant. Accordingly, it was concluded that the tactile comfort of denim fabrics can be estimated with a high precision, based on the results of in-plane shear behavior measurements.

Keywords: denim fabrics, in-plane shear behavior, linear regression estimation, tactile comfort

Procedia PDF Downloads 302