Search results for: generalized mathematical model

Authors: Stefano M. Spagocci

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The efficiency of photovoltaic panels can be calculated with such software packages as RETScreen that allow design engineers to take financial as well as technical considerations into account. RETScreen is interfaced with meteorological databases, so that efficiency calculations can be realistically carried out. The author has recently contributed to the development of solar modules with accumulation capability and an embedded water purifier, aimed at off-grid users such as users in developing countries. The software packages examined do not allow to take ancillary equipment into account, hence the decision to implement a technical and financial model of the system. The author realized that, rather than re-implementing the quite sophisticated model of RETScreen - a mathematical description of which is anyway not publicly available - it was possible to drastically simplify it, including the meteorological factors which, in RETScreen, are presented in a numerical form. The day-by-day efficiency of a photovoltaic solar panel was parametrized by the product of factors expressing, respectively, daytime duration, solar right ascension motion, solar declination motion, cloudiness, temperature. For the sun-motion-dependent factors, positional astronomy formulae, simplified by the author, were employed. Meteorology-dependent factors were fitted by simple trigonometric functions, employing numerical data supplied by RETScreen. The accuracy of our model was tested by comparing it to the predictions of RETScreen; the accuracy obtained was 11%. In conclusion, our study resulted in a model that can be easily implemented in a spreadsheet - thus being easily manageable by non-specialist personnel - or in more sophisticated software packages. The model was used in a number of design exercises, concerning photovoltaic solar panels and ancillary equipment like the above-mentioned water purifier.

Keywords: clean energy, energy engineering, mathematical modelling, photovoltaic panels, solar energy

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Authors: F. R. M. Nascimento, E. E. S. Lora, J. C. E. Palácio

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A mathematical model to investigate the performance of a two stage fixed bed downdraft gasifier operating with air, steam and oxygen mixtures as the gasifying fluid has been developed. The various conditions of mixtures for a double stage fluid entry, have been performed. The model has been validated through a series of experimental tests performed by NEST – The Excellence Group in Thermal and Distributed Generation of the Federal University of Itajubá. Influence of mixtures are analyzed through the Steam to Biomass (SB), Equivalence Ratio (ER) and the Oxygen Concentration (OP) parameters in order to predict the best operating conditions to obtain adequate output gas quality, once is a key parameter for subsequent gas processing in the synthesis of biofuels, heat and electricity generation. Results show that there is an optimal combination in the steam and oxygen content of the gasifying fluid which allows the user find the best conditions to design and operate the equipment according to the desired application.

Keywords: air, equilibrium, downdraft, fixed bed gasification, mathematical modeling, mixtures, oxygen steam

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Authors: Tariq Aljuneidi, Akif Asil Bulgak

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Remanufacturing may be defined as the process of bringing used products to “like-new” functional state with warranty to match, and it is one of the most popular product end-of-life scenarios. An efficient remanufacturing network lead to an efficient design of sustainable manufacturing enterprise. In remanufacturing network, products are collected from the customer zone, disassembled and remanufactured at a suitable remanufacturing facility. In this respect, another issue to consider is how the returned product to be remanufactured, in other words, what is the best layout for such facility. In order to achieve a sustainable manufacturing system, Cellular Manufacturing System (CMS) designs are highly recommended, CMSs combine high throughput rates of line layouts with the flexibility offered by functional layouts (job shop). Introducing the CMS while designing a remanufacturing network will benefit the utilization of such a network. This paper presents and analyzes a comprehensive mathematical model for the design of Dynamic Cellular Remanufacturing Systems (DCRSs). In this paper, the proposed model is the first one to date that consider CMS and remanufacturing system simultaneously. The proposed DCRS model considers several manufacturing attributes such as multi-period production planning, dynamic system reconfiguration, duplicate machines, machine capacity, available time for workers, worker assignments, and machine procurement, where the demand is totally satisfied from a returned product. A numerical example is presented to illustrate the proposed model.

Keywords: cellular manufacturing system, remanufacturing, mathematical programming, sustainability

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Authors: Shahul Hamid Khan, S. Santhosh, Abhinav Kumar Sharma

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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. Bi-objective mathematical models for total cost and total emission for the entire forward supply chain are considered. Here five different problems are considered by varying the number of suppliers, manufacturers, and environmental levels, for illustrating the taken mathematical model. GA, and Random search are used for finding the optimal solution. The input parameters of the optimal solution are used to find the tradeoff between the initial investment by the industry and the long term benefit of the environment.

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

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Authors: Lely A. Luengas, Pedro R. Vizcaya, Giovanni Sánchez

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In this paper, a methodology is presented to obtain the Static Alignment Model for any transtibial amputee person. The proposed methodology starts from experimental data collected on the Hospital Militar Central, Bogotá, Colombia. The effects of transtibial prosthesis malalignment on amputees were measured in terms of joint angles, center of pressure (COP) and weight distribution. Some statistical tools are used to obtain the model parameters. Mathematical predictive models of prosthetic alignment were created. The proposed models are validated in amputees and finding promising results for the prosthesis Static Alignment. Static alignment process is unique to each subject; nevertheless the proposed methodology can be used in each transtibial amputee.

Keywords: information theory, prediction model, prosthetic alignment, transtibial prosthesis

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Authors: Danielle M. Barna, Kolbjørn Engeland, Thordis Thorarinsdottir, Chong-Yu Xu

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Design flood values give estimates of flood magnitude within a given return period and are essential to making adaptive decisions around land use planning, infrastructure design, and disaster mitigation. Often design flood values are needed at locations with insufficient data. Additionally, in hydrologic applications where flood retention is important (e.g., floodplain management and reservoir design), design flood values are required at different flood durations. A statistical approach to this problem is a development of a regression model for extremes where some of the parameters are dependent on flood duration in addition to being covariate-dependent. In hydrology, this is called a regional flood-duration-frequency (regional-QDF) model. Typically, the underlying statistical distribution is chosen to be the Generalized Extreme Value (GEV) distribution. However, as the support of the GEV distribution depends on both its parameters and the range of the data, special care must be taken with the development of the regional model. In particular, we find that the GEV is problematic when developing a GAMLSS-type analysis due to the difficulty of proposing a link function that is independent of the unknown parameters and the observed data. We discuss these challenges in the context of developing a regional QDF model for Norway.

Keywords: design flood values, bayesian statistics, regression modeling of extremes, extreme value analysis, GEV

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Authors: Moses Aron, Elias Mwakilama, Jimmy Namangale

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Spending more time on long queues for a basic service remains a common challenge to most developing countries, including Malawi. For health sector in particular, Out-Patient Department (OPD) experiences long queues. This puts the lives of patients at risk. However, using queuing analysis to under the nature of the problems and efficiency of service systems, such problems can be abated. Based on a kind of service, literature proposes different possible queuing models. However, unlike using generalized assumed models proposed by literature, use of real time case study data can help in deeper understanding the particular problem model and how such a model can vary from one day to the other and also from each case to another. As such, this study uses data obtained from one urban HC for BP, Pediatric and General OPD cases to investigate an average queuing time for patients within the system. It seeks to highlight the proper queuing model by investigating the kind of distributions functions over patient’s arrival time, inter-arrival time, waiting time and service time. Comparable with the standard set values by WHO, the study found that patients at this HC spend more waiting times than service times. On model investigation, different days presented different models ranging from an assumed M/M/1, M/M/2 to M/Er/2. As such, through sensitivity analysis, in general, a commonly assumed M/M/1 model failed to fit the data but rather an M/Er/2 demonstrated to fit well. An M/Er/3 model seemed to be good in terms of measuring resource utilization, proposing a need to increase medical personnel at this HC. However, an M/Er/4 showed to cause more idleness of human resources.

Keywords: health care, out-patient department, queuing model, sensitivity analysis

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.

Keywords: Adomian, decomposition method, generalized thermoelasticity, algorithm

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Authors: Farhad Salek, Shahaboddin Resalati

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The production of electric vehicles (EVs) featuring lithium-ion battery technology has substantially escalated over the past decade, demonstrating a steady and persistent upward trajectory. The imminent retirement of electric vehicle (EV) batteries after approximately eight years underscores the critical need for their redirection towards recycling, a task complicated by the current inadequacy of recycling infrastructures globally. A potential solution for such concerns involves extending the operational lifespan of electric vehicle (EV) batteries through their utilization in stationary energy storage systems during secondary applications. Such adoptions, however, require addressing the safety concerns associated with batteries’ knee points and thermal runaways. This paper develops an accurate mathematical model representative of the second-life battery packs from a cell-to-pack scale using an equivalent circuit model (ECM) methodology. Neural network algorithms are employed to forecast the degradation parameters based on the EV batteries' aging history to develop a degradation model. The degradation model is integrated with the ECM to reflect the impacts of the cycle aging mechanism on battery parameters during operation. The developed model is tested under real-life load profiles to evaluate the life span of the batteries in various operating conditions. The methodology and the algorithms introduced in this paper can be considered the basis for Battery Management System (BMS) design and techno-economic analysis of such technologies.

Keywords: second life battery, electric vehicles, degradation, neural network

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Authors: Muhammad Fiaz

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The article in hand is the study of complex features like Zero Hopf Bifurcation, Chaos and Synchronization of integer and fractional order version of a new 3D finance system. Trusted tools of averaging theory and active control method are utilized for investigation of Zero Hopf bifurcation and synchronization for both versions respectively. Inventiveness of the paper is to find the answer of a question that is it possible to find a chaotic system which can be synchronized with any other of the same dimension? Based on different examples we categorically develop a theory that if a couple of master and slave chaotic dynamical system is synchronized by selecting a suitable gain matrix with special conditions then the master system is synchronized with any chaotic dynamical system of the same dimension. With the help of this study we developed generalized theorems for synchronization of n-dimension dynamical systems for integer as well as fractional versions. it proposed that this investigation will contribute a lot to control dynamical systems and only a suitable gain matrix with special conditions is enough to synchronize the system under consideration with any other chaotic system of the same dimension. Chaotic properties of fractional version of the new finance system are also analyzed at fractional order q=0.87. Simulations results, where required, also provided for authenticity of analytical study.

Keywords: complex analysis, chaos, generalized synchronization, control dynamics, fractional order analysis

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Authors: Temur Chilachava

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In work the new nonlinear mathematical model describing assimilation of the people (population) with some less widespread language by two states with two various widespread languages, taking into account demographic factor is offered. In model three subjects are considered: the population and government institutions with the widespread first language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the population and government institutions with the widespread second language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the third population (probably small state formation, an autonomy), exposed to bilateral assimilation from two rather powerful states. Earlier by us it was shown that in case of zero demographic factor of all three subjects, the population with less widespread language completely assimilates the states with two various widespread languages, and the result of assimilation (redistribution of the assimilated population) is connected with initial quantities, technological and economic capabilities of the assimilating states. In considered model taking into account demographic factor natural decrease in the population of the assimilating states and a natural increase of the population which has undergone bilateral assimilation is supposed. At some ratios between coefficients of natural change of the population of the assimilating states, and also assimilation coefficients, for nonlinear system of three differential equations are received the two first integral. Cases of two powerful states assimilating the population of small state formation (autonomy), with different number of the population, both with identical and with various economic and technological capabilities are considered. It is shown that in the first case the problem is actually reduced to nonlinear system of two differential equations describing the classical model "predator - the victim", thus, naturally a role of the victim plays the population which has undergone assimilation, and a predator role the population of one of the assimilating states. The population of the second assimilating state in the first case changes in proportion (the coefficient of proportionality is equal to the relation of the population of assimilators in an initial time point) to the population of the first assimilator. In the second case the problem is actually reduced to nonlinear system of two differential equations describing type model "a predator – the victim", with the closed integrated curves on the phase plane. In both cases there is no full assimilation of the population to less widespread language. Intervals of change of number of the population of all three objects of model are found. The considered mathematical models which in some approach can model real situations, with the real assimilating countries and the state formations (an autonomy or formation with the unrecognized status), undergone to bilateral assimilation, show that for them the only possibility to avoid from assimilation is the natural demographic increase in population and hope for natural decrease in the population of the assimilating states.

Keywords: nonlinear mathematical model, bilateral assimilation, demographic factor, first integrals, result of assimilation, intervals of change of number of the population

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Authors: Anuruddha Jayasuriya, Thanakorn Pheeraphan

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In this paper, a review of different mathematical models which can be used as prediction tools to assess the time to crack reinforced concrete (RC) due to corrosion is investigated. This investigation leads to an experimental study to validate a selected prediction model. Most of these mathematical models depend upon the mechanical behaviors, chemical behaviors, electrochemical behaviors or geometric aspects of the RC members during a corrosion process. The experimental program is designed to verify the accuracy of a well-selected mathematical model from a rigorous literature study. Fundamentally, the experimental program exemplifies both one-dimensional chloride diffusion using RC squared slab elements of 500 mm by 500 mm and two-dimensional chloride diffusion using RC squared column elements of 225 mm by 225 mm by 500 mm. Each set consists of three water-to-cement ratios (w/c); 0.4, 0.5, 0.6 and two cover depths; 25 mm and 50 mm. 12 mm bars are used for column elements and 16 mm bars are used for slab elements. All the samples are subjected to accelerated chloride corrosion in a chloride bath of 5% (w/w) sodium chloride (NaCl) solution. Based on a pre-screening of different models, it is clear that the well-selected mathematical model had included mechanical properties, chemical and electrochemical properties, nature of corrosion whether it is accelerated or natural, and the amount of porous area that rust products can accommodate before exerting expansive pressure on the surrounding concrete. The experimental results have shown that the selected model for both one-dimensional and two-dimensional chloride diffusion had ±20% and ±10% respective accuracies compared to the experimental output. The half-cell potential readings are also used to see the corrosion probability, and experimental results have shown that the mass loss is proportional to the negative half-cell potential readings that are obtained. Additionally, a statistical analysis is carried out in order to determine the most influential factor that affects the time to corrode the reinforcement in the concrete due to chloride diffusion. The factors considered for this analysis are w/c, bar diameter, and cover depth. The analysis is accomplished by using Minitab statistical software, and it showed that cover depth is the significant effect on the time to crack the concrete from chloride induced corrosion than other factors considered. Thus, the time predictions can be illustrated through the selected mathematical model as it covers a wide range of factors affecting the corrosion process, and it can be used to predetermine the durability concern of RC structures that are vulnerable to chloride exposure. And eventually, it is further concluded that cover thickness plays a vital role in durability in terms of chloride diffusion.

Keywords: accelerated corrosion, chloride diffusion, corrosion cracks, passivation layer, reinforcement corrosion

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Authors: Amares Chattopadhyay, Akanksha Srivastava

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A unified approach to study the reflection of a plane wave in three-dimensional model comprised of the triclinic viscoelastic medium. The phase velocities of reflected qP, qSV and qSH wave have been calculated for the concerned medium by using the eigenvalue approach. The generalized method has been implemented to compute the complex form of amplitude ratios. Further, we discussed the nature of reflection coefficients of qP, qSV and qSH wave. The viscoelastic parameter, polar angle and azimuthal angle are found to be strongly influenced by amplitude ratios. The research article is particularly focused to study the effect of viscoelasticity associated with highly anisotropic media which exhibits the notable information about the reflection coefficients of qP, qSV, and qSH wave. The outcomes may further useful to the better exploration of all types of hydrocarbon reservoir and advancement in the field of reflection seismology.

Keywords: amplitude ratios, three dimensional, triclinic, viscoelastic

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Authors: Jagdish Prasad Maurya, Sanjay Kumar Pandey

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Inadequate understanding of the complex nature of flow features in tornado vortex is a major problem in modelling tornadoes. Tornadoes are violent atmospheric phenomenon that appear all over the world. Modelling tornadoes aim to reduce the loss of the human lives and material damage caused by the tornadoes. Dynamics of tornado is investigated by a numerical technique, the improved version of the projection method. In this paper, authors solve the problem for axisymmetric tornado vortex by the said method that uses a finite difference approach for getting an accurate and stable solution. The conclusions drawn are that large radial inflow velocity occurs near the ground that leads to increase the tangential velocity. The increased velocity phenomenon occurs close to the boundary and absolute maximum wind is obtained near the vortex core. The results validate previous numerical and theoretical models.

Keywords: computational fluid dynamics, mathematical model, Navier-Stokes equations, tornado

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Authors: Komon Paisal

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The purposes of this research were (1) to create a learning activity for constructivism, (2) study the Mathematical Analysis courses learning achievement, and (3) study students’ attitude toward the learning activity for constructivism. The samples in this study were divided into 2 parts including 3 Mathematical Analysis courses instructors of Suan Sunandha Rajabhat University who provided basic information and attended the seminar and 17 Mathematical Analysis courses students who were studying in the academic and engaging in the learning activity for constructivism. The research instruments were lesson plans constructivism, subjective Mathematical Analysis courses achievement test with reliability index of 0.8119, and an attitude test concerning the students’ attitude toward the Mathematical Analysis courses learning activity for constructivism. The result of the research show that the efficiency of the Mathematical Analysis courses learning activity for constructivism is 73.05/72.16, which is more than expected criteria of 70/70. The research additionally find that the average score of learning achievement of students who engaged in the learning activities for constructivism are equal to 70% and the students’ attitude toward the learning activity for constructivism are at the medium level.

Keywords: constructivism, learning management, mathematics analysis courses, learning activity

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Authors: Abdullah Eqal Al Mazrooei

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In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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Authors: Oren Shtayermman

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The current investigation expended on research among parents caring for a child who is diagnosed with an autism spectrum disorder (ASD). An online web survey was used to collect data from 253 parents caring for a child with a diagnosis of ASD. Both parents reported on elevated levels of parental stress associated with caring for the child on the spectrum. In addition, lower levels of marital satisfaction were found in both parents. About 13% of the parents in the sample met the diagnostic criteria for Major Depressive Disorder and About 15% of the parents met the diagnostic criteria for Generalized Anxiety Disorder. Although the majority of the sample was females (94%) significant differences were found between males and females in relation to meeting the diagnostic criteria for Major Depressive Disorder and for Generalized Anxiety Disorder. Higher levels of stress were associated with higher number of Generalized Anxiety Disorder symptoms and higher number of Major Depressive Disorder symptoms. Findings from this study indicate how vulnerable parents and especially females are in relation to caring to a child diagnosed with ASD. Educational Objectives: At the conclusion of the paper, the readers should be able to: -Identify levels of stress and marital satisfaction among parents caring for a child diagnosed with autism spectrum disorder, -Recognize the impact of stress on the development of mental health issues, -Name the two most common mood and anxiety related disorders associated with caring for a child diagnosed with an autism spectrum disorder.

Keywords: autism, stress, parents, children

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Authors: S. Belhour, A. K. Ferouani, C. Azizi

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In recent years, a considerable effort (experience, numerical simulation, and theoretical prediction models) has characterised by high efficiency and low cost. Then an improved physics analytical model for simulating is proposed. The performance of GaAs MESFETs has been developed for use in device design for high frequency. This model is based on mathematical analysis, and a new approach for the standard model is proposed, this approach allowed to conceive applicable model for MESFET’s operating in the turn-one or pinch-off region and valid for the short-channel and the long channel MESFET’s in which the two dimensional potential distribution contributed by the depletion layer under the gate is obtained by conventional approximation. More ever, comparisons between the analytical models with different values of mobility are proposed, and a good agreement is obtained.

Keywords: analytical, gallium arsenide, MESFET, mobility, models

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Authors: M. Benachour, N. Benachour, M. Benguediab

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In this investigation, variation of cyclic loading effect on fatigue crack growth is studied. This study is performed on 2024 T351 and 7050-T74 aluminum alloys, used in aeronautical structures. The propagation model used in this study is NASGRO model. In constant amplitude loading (CA), the effect of stress ratio has been investigated. Fatigue life and fatigue crack growth rate were affected by this factor. Results showed an increasing in fatigue crack growth rates (FCGRs) with increasing stress ratio. Variable amplitude loading (VAL) can take many forms i.e with a single overload, overload band etc. The shape of these loads affects strongly the fracture life and FCGRs. The application of a single overload (ORL) decrease the FCGR and increase the delay crack length caused by the formation of a larger plastic zone compared to the plastic zone due without VAL. The fatigue behavior of the both material under single overload has been compared.

Keywords: fatigue crack growth, overload ratio, stress ratio, generalized willenborg model, retardation, al-alloys

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Authors: Laura C. Dapp, Claudia M. Roebers

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Being physically active has many benefits for children and adolescents. It is crucial for various aspects of physical and mental health, the development of a healthy self-concept, and also positively influences academic performance and school achievement. In addressing the still incomplete understanding of the link between physical activity (PA) and academic achievement, the current study scrutinized the open issue of how PA has to be implemented to positively affect mathematical outcomes in N = 138 fourth graders. Therefore, the current study distinguished between structured PA (formal, organized, adult-led exercise and deliberate sports practice) and unstructured PA (non-formal, playful, peer-led physically active play and sports activities). Results indicated that especially structured PA has the potential to contribute to mathematical outcomes. Although children spent almost twice as much time engaging in unstructured PA as compared to structured PA, only structured PA was significantly related to mathematical achievement as well as to mathematical self-concept. Furthermore, the pending issue concerning the quantity of PA needed to enhance children’s mathematical achievement was addressed. As to that, results indicated that the amount of time spent in structured PA constitutes a critical factor in accounting for mathematical outcomes, since children engaging in PA for two hours or more a week were shown to be both the ones with the highest mathematical self-concept as well as those attaining the highest mathematical achievement scores. Finally, the present study investigated the indirect effect of PA on mathematical achievement by controlling for the mathematical self-concept as a mediating variable. The results of a maximum likelihood mediation analysis with a 2’000 resampling bootstrapping procedure for the 95% confidence intervals revealed a full mediation, indicating that PA improves mathematical self-concept, which, in turn, positively affects mathematical achievement. Thus, engaging in high amounts of structured PA constitutes an advantageous leisure activity for children and adolescents, not only to enhance their physical health but also to foster their self-concept in a way that is favorable and encouraging for promoting their academic achievement. Note: The content of this abstract is partially based on a paper published elswhere by the authors.

Keywords: Academic Achievement, Mathematical Performance, Physical Activity, Self-Concept

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Authors: I. M. L. Nadeesha Jayaweera, Adao Alex Trindade

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In choosing a candidate model in likelihood-based modeling via an information criterion, the practitioner is often faced with the difficult task of deciding just how far up the ranked list to look. Motivated by this pragmatic necessity, we construct an uncertainty band for a generalized (model selection) information criterion (GIC), defined as a criterion for which the limit in probability is identical to that of the normalized log-likelihood. This includes common special cases such as AIC & BIC. The method starts from the asymptotic normality of the GIC for the joint distribution of the candidate models in an independent and identically distributed (IID) data framework and proceeds by deriving the (asymptotically) exact distribution of the minimum. The calculation of an upper quantile for its distribution then involves the computation of multivariate Gaussian integrals, which is amenable to efficient implementation via the R package "mvtnorm". The performance of the methodology is tested on simulated data by checking the coverage probability of nominal upper quantiles and compared to the bootstrap. Both methods give coverages close to nominal for large samples, but the bootstrap is two orders of magnitude slower. The methodology is subsequently extended to two other commonly used model structures: regression and time series. In the regression case, we derive the corresponding asymptotically exact distribution of the minimum GIC invoking Lindeberg-Feller type conditions for triangular arrays and are thus able to similarly calculate upper quantiles for its distribution via multivariate Gaussian integration. The bootstrap once again provides a default competing procedure, and we find that similar comparison performance metrics hold as for the IID case. The time series case is complicated by far more intricate asymptotic regime for the joint distribution of the model GIC statistics. Under a Gaussian likelihood, the default in most packages, one needs to derive the limiting distribution of a normalized quadratic form for a realization from a stationary series. Under conditions on the process satisfied by ARMA models, a multivariate normal limit is once again achieved. The bootstrap can, however, be employed for its computation, whence we are once again in the multivariate Gaussian integration paradigm for upper quantile evaluation. Comparisons of this bootstrap-aided semi-exact method with the full-blown bootstrap once again reveal a similar performance but faster computation speeds. One of the most difficult problems in contemporary statistical methodological research is to be able to account for the extra variability introduced by model selection uncertainty, the so-called post-model selection inference (PMSI). We explore ways in which the GIC uncertainty band can be inverted to make inferences on the parameters. This is being attempted in the IID case by pivoting the CDF of the asymptotically exact distribution of the minimum GIC. For inference one parameter at a time and a small number of candidate models, this works well, whence the attained PMSI confidence intervals are wider than the MLE-based Wald, as expected.

Keywords: model selection inference, generalized information criteria, post model selection, Asymptotic Theory

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Authors: Selahattin Gultekin

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Today, in engineering departments, mathematics courses such as calculus, linear algebra and differential equations are generally taught by mathematicians. Therefore, during mathematicians’ classroom teaching there are few or no applications of the concepts to real world problems at all. Most of the times, students do not know whether the concepts or rules taught in these courses will be used extensively in their majors or not. This situation holds true of for all engineering and science disciplines. The general trend toward these mathematic courses is not good. The real-life application of mathematics will be appreciated by students when mathematical modeling of real-world problems are tackled. So, students do not like abstract mathematics, rather they prefer a solid application of the concepts to our daily life problems. The author highly recommends that mathematical modeling is to be taught starting in high schools all over the world In this paper, some mathematical concepts such as limit, derivative, integral, Taylor Series, differential equations and mean-value-theorem are chosen and their applications with graphical representations to real problems are emphasized.

Keywords: applied mathematics, engineering mathematics, mathematical concepts, mathematical modeling

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Authors: Elena M. Kopteva, Pavlina Jaluvkova, Zdenek Stuchlik

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In spite of the numerous attempts to close the discussion about the influence of cosmological expansion on local gravitationally bounded systems, this question arises in literature again and again and remains still far from its final resolution. Here one of the main problems is the problem of obtaining a physically adequate model of strongly gravitating object immersed in non-static cosmological background. Such objects are usually called ‘cosmological’ black holes and are of great interest in wide set of cosmological and astrophysical areas. In this work the set of new exact solutions of the Einstein equations is derived for the flat space that generalizes the known Lemaitre-Tolman-Bondi solution for the case of nonzero pressure. The solutions obtained are pretending to describe the black hole immersed in nonstatic cosmological background and give a possibility to investigate the hot problems concerning the effects of the cosmological expansion in gravitationally bounded systems, the structure formation in the early universe, black hole thermodynamics and other related problems. It is shown that each of the solutions obtained contains either the Reissner-Nordstrom or the Schwarzschild black hole in the central region of the space. It is demonstrated that the approach of the mass function use in solving of the Einstein equations allows clear physical interpretation of the resulting solutions, that is of much benefit to any their concrete application.

Keywords: exact solutions of the Einstein equations, cosmological black holes, generalized Lemaitre-Tolman-Bondi solutions, nonzero pressure

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Authors: Pakhapoom Sarapat, James M. Hill, Duangkamon Baowan

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Carbon nanotori provide several properties such as high tensile strength and heat resistance. They are promised to be ideal structures for encapsulation, and their encapsulation ability can be determined by the interaction energy between the carbon nanotori and the encapsulated nanostructures. Such interaction energy is evaluated using Lennard-Jones potential and continuum approximation. Here, four problems relating to toroidal molecules are determined in order to find the most stable configuration. Firstly, the interaction energy between a carbon nanotorus and an atom is examined. The second problem relates to the energy of a fullerene encapsulated inside a carbon nanotorus. Next, the interaction energy between two symmetrically situated and parallel nanotori is considered. Finally, the classical mechanics is applied to model the interaction energy between the toroidal structure of cyclodextrin and the spherical DNA molecules. These mathematical models might be exploited to study a number of promising devices for future developments in bio and nanotechnology.

Keywords: carbon nanotori, continuum approximation, interaction energy, Lennard-Jones potential, nanotechnology

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Authors: Johna Bernice Ablaza, Bryan Lim Corpuz, Joanna Marie Estrada, Mary Ann Cristine Olgado, Rhina Recato

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This study aimed to describe the mathematical beliefs and attitudes in relation to the mathematics performance of freshman college students. The descriptive design using the correlational study was used to describe the relationship among mathematical beliefs, attitudes, and performance of freshman college students. This study involved one hundred fifty (150) freshman college students of Philippine Normal University during the third trimester of school year 2015-2016. The research instruments used to gather the information needed in the study are the beliefs about Mathematics Questionnaire, the KIM-Project Questionnaire, and the ACT Compass Mathematics Test. The data gathered were analyzed using the percentages, mean, standard deviation, and Pearson r-moment correlation. The results of this study have shown that although students believe that Mathematics is significant in their lives, the overall result on their beliefs and attitudes are positively low. There is a significant relationship between the students’ mathematical beliefs and mathematics performance. Likewise, their attitudes in mathematics have significant relationship to mathematics performance.

Keywords: attitudes, diligence, interest, mathematical beliefs, mathematical performance, self-confidence

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Authors: N. Bazyar Shourabi, K. Nyarko, C. Scott, M. Jeihnai

Abstract:

Ground drones have the potential to reduce the cost and time of making last-mile deliveries. They also have the potential to make a huge impact on human life. Despite this potential, little work has gone into developing a suitable feasibility model for ground drone delivery in dense urban areas. Today, most of the experimental ground delivery drones utilize sidewalks only, with just a few of them starting to use bike lanes, which a significant portion of some urban areas have. This study works on the feasibility of using bike lanes in conjunction with sidewalks for ground drone applications in last-mile delivery for dense urban areas. This work begins with surveying bike lanes and sidewalks within the city of Boston using Geographic Information System (GIS) software to determine the percentage of coverage currently available within the city. Then six scenarios are examined. Based on this research, a mathematical model is developed. The daily cost of delivering packages using each scenario is calculated by the mathematical model. Comparing the drone delivery scenarios with the traditional method of package delivery using trucks will provide essential information concerning the feasibility of implementing routing protocols that combine the use of sidewalks and bike lanes. The preliminary results of the model show that ground drones that can travel via sidewalks or bike lanes have the potential to significantly reduce delivery cost.

Keywords: ground drone, intelligent transportation system, last-mile delivery, sidewalk robot

Procedia PDF Downloads 112

Authors: Khin Fai Chen, Jee-Hou Ho, Eng Hwa Yap

Abstract:

An acoustic micro-energy harvester (AMEH) is developed to convert wasted acoustical energy into useful electrical energy. AMEH is mathematically modeled using lumped element modelling (LEM) and Euler-Bernoulli beam (EBB) modelling. An experiment is designed to validate the mathematical model and assess the feasibility of AMEH. Comparison of theoretical and experimental data on critical parameter value such as Mm, Cms, dm and Ceb showed the variances are within 1% to 6%, which is reasonably acceptable. Hence, AMEH mathematical model is validated. Then, AMEH undergoes bandwidth tuning for performance optimization for further experimental work. The AMEH successfully produces 0.9 V⁄(m⁄s^2) and 1.79 μW⁄(m^2⁄s^4) at 60Hz and 400kΩ resistive load which only show variances about 7% compared to theoretical data. By integrating a capacitive load of 200µF, the discharge cycle time of AMEH is 1.8s and the usable energy bandwidth is available as low as 0.25g. At 1g and 60Hz resonance frequency, the averaged power output is about 2.2mW which fulfilled a range of wireless sensors and communication peripherals power requirements. Finally, the design for AMEH is assessed, validated and deemed as a feasible design.

Keywords: piezoelectric, acoustic, energy harvester

Procedia PDF Downloads 266

Authors: Nqobile Muleya, Winston Garira, Godwin Mchau

Abstract:

Citrus Black Spot (CBS) is a fungal disease that is responsible for huge economical loss and poses a threat to the citrus industry worldwide. We construct a mathematical model framework for citrus black spot between fruits to characterise the dynamics of the disease development, paying attention to the pathogen life cycle. We have made an observation from the model analysis that the initial inoculum from ascomata is very important for disease development and thereafter it is no longer important due to conidia which is responsible for secondary infection. Most importantly, the model indicated that ascospores and conidia are very important parameters in developing citrus black spot within a short distance. The basic reproductive number and its importance in relation to citrus black spot persistence are outlined. A numerical simulation of the model was done to explain the theoretical findings.

Keywords: epidemiological modelling, Guidnardia citricarpa, life cycle stage, fungal, disease development

Procedia PDF Downloads 344

Authors: Asadullah I. Qazi, Mansoor Ahsan, Zahir Ashraf, Uzair Ahmad

Abstract:

System identification of an Unmanned Aerial Vehicle (UAV), to acquire its mathematical model, is a significant step in the process of aircraft flight automation. The need for reliable mathematical model is an established requirement for autopilot design, flight simulator development, aircraft performance appraisal, analysis of aircraft modifications, preflight testing of prototype aircraft and investigation of fatigue life and stress distribution etc.  This research is aimed at system identification of a fixed wing UAV by means of specifically designed flight experiment. The purposely designed flight maneuvers were performed on the UAV and aircraft states were recorded during these flights. Acquired data were preprocessed for noise filtering and bias removal followed by parameter estimation of longitudinal dynamics transfer functions using MATLAB system identification toolbox. Black box identification based transfer function models, in response to elevator and throttle inputs, were estimated using least square error   technique. The identification results show a high confidence level and goodness of fit between the estimated model and actual aircraft response.

Keywords: fixed wing UAV, system identification, black box modeling, longitudinal dynamics, least square error

Procedia PDF Downloads 306

Authors: Arunee Wongkhao, Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper, we propose two new confidence intervals for the difference between the inverse of normal means with known coefficients of variation. One of these two confidence intervals for this problem is constructed based on the generalized confidence interval and the other confidence interval is constructed based on the closed form method of variance estimation. We examine the performance of these confidence intervals in terms of coverage probabilities and expected lengths via Monte Carlo simulation.

Keywords: coverage probability, expected length, inverse of normal mean, coefficient of variation, generalized confidence interval, closed form method of variance estimation

Procedia PDF Downloads 291