Search results for: mathematical proportions

Authors: Amira Abdelrasoul, Huu Doan, Ali Lohi

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An efficient and well-planned ultrafiltration process is becoming a necessity for monetary returns in the industrial settings. The aim of the present study was to develop a mathematical model for an accurate prediction of ultrafiltration membrane fouling of latex effluent applied to homogeneous and heterogeneous membranes with uniform and non-uniform pore sizes, respectively. The models were also developed for an accurate prediction of power consumption that can handle the large-scale purposes. The model incorporated the fouling attachments as well as chemical and physical factors in membrane fouling for accurate prediction and scale-up application. Both Polycarbonate and Polysulfone flat membranes, with pore sizes of 0.05 µm and a molecular weight cut-off of 60,000, respectively, were used under a constant feed flow rate and a cross-flow mode in ultrafiltration of the simulated paint effluent. Furthermore, hydrophilic ultrafilic and hydrophobic PVDF membranes with MWCO of 100,000 were used to test the reliability of the models. Monodisperse particles of 50 nm and 100 nm in diameter, and a latex effluent with a wide range of particle size distributions were utilized to validate the models. The aggregation and the sphericity of the particles indicated a significant effect on membrane fouling.

Keywords: membrane fouling, mathematical modeling, power consumption, attachments, ultrafiltration

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Authors: M. Khoshab, M. J. Sedigh

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Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.

Keywords: dynamic system, lag on supply demand, market stability, supply demand model

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Authors: Jitendra Singh, Vivek Kumar

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In this paper, a susceptible infective susceptible mathematical model is proposed and analyzed where the migration of human population is given by migration function. It is assumed that the disease is transmitted by direct contact of susceptible and infective populations with constant contact rate. The equilibria and their stability are studied by using the stability theory of ordinary differential equations and computer simulation. The model analysis shows that the spread of infectious disease increases when human population immigration increases in the habitat but it decreases if emigration increases.

Keywords: SIS (Susceptible Infective Susceptible) model, migration function, susceptible, stability

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Authors: Amanbek Jainakov, Abdikerim Kurbanaliev

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The work presents the results of mathematical modeling of large-scale flows in areas with a complex topographic relief. The Reynolds-averaged Navier—Stokes equations constitute the basis of the three-dimensional unsteady modeling. The well-known Volume of Fluid method implemented in the solver interFoam of the open package OpenFOAM 2.3 is used to track the free-boundary location. The mathematical model adequacy is checked by comparing with experimental data. The efficiency of the applied technology is illustrated by the example of modeling the breakthrough of the dams of the Andijan (Uzbekistan) and Papan (near the Osh town, Kyrgyzstan) reservoir.

Keywords: three-dimensional modeling, free boundary, the volume-of-fluid method, dam break, flood, OpenFOAM

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Authors: B. Afsari, M. Hassanpour, M. Shabani

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This study aimed to investigate the phase morphology of ternary blends comprising PP, PA6, and a blend of EPDM and EPDM-g-MA in a 70/15/15 ratio. Varying ratios of EPDM to EPDM-g-MA were examined. As the proportion of EPDM-g-MA increased, an interlayer phase formed between the dispersed PA6 domains and the PP matrix. This resulted in the development of a core-shell encapsulation morphology within the blends. The concentration of the EPDM-g-MA component is inversely correlated with the average size of PA6 particles. Additionally, blends containing higher proportions of the EPDM-g-MA rubbery phase exhibited an aggregated structure of the modifier particles. Notably, as the concentration of EPDM-g-MA increased from 0% to 15% in the blend, there was a consistent monotonic reduction in the size of PA6 particles.

Keywords: phase morphology, rubbery phase, rubber functionality, ternary blends

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Authors: Flavio Araujo, Paulo Scalize, Julio Lima, Natalia Vieira, Antonio Albuquerque, Isabela Santos

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From a concern regarding the environmental impacts caused by the disposal of residues generated in Water Treatment Plants (WTP's), alternatives ways have been studied to use these residues as raw material for manufacture of building materials, avoiding their discharge on water streams, disposal on sanitary landfills or incineration. This paper aims to present the results of a research work, which is using WTR for replacing the soil content in the manufacturing of soil-cement floor with proportions of 0, 5, 10 and 15%. The samples tests showed a reduction mechanical strength in so far as has increased the amount of waste. The water absorption was below the maximum of 6% required by the standard. The application of WTR contributes to the reduction of the environmental damage in the water treatment industry.

Keywords: residue, soil-cement floor, sustainable, WTP

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: Tala Toonsi, Marah Alagha, Lina Alnowaiser, Hala Rajab

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This report is about the Photomath app, which is an AI application that uses image recognition technology, specifically optical character recognition (OCR) algorithms. The (OCR) algorithm translates the images into a mathematical equation, and the app automatically provides a step-by-step solution. The application supports decimals, basic arithmetic, fractions, linear equations, and multiple functions such as logarithms. Testing was conducted to examine the usage of this app, and results were collected by surveying ten participants. Later, the results were analyzed. This paper seeks to answer the question: To what level the artificial intelligence features are accurate and the speed of process in this app. It is hoped this study will inform about the efficiency of AI in Photomath to the users.

Keywords: photomath, image recognition, app, OCR, artificial intelligence, mathematical equations.

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Authors: Javad Khaligh, Aghileh Heydari, Ali Akbar Heydari

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Mathematical epidemiological models for the spread of disease through a population are used to predict the prevalence of a disease or to study the impacts of treatment or prevention measures. Initial conditions for these models are measured from statistical data collected from a population since these initial conditions can never be exact, the presence of chaos in mathematical models has serious implications for the accuracy of the models as well as how epidemiologists interpret their findings. This paper confirms the chaotic behavior of a model for dengue fever and SI by investigating sensitive dependence, bifurcation, and 0-1 test under a variety of initial conditions.

Keywords: epidemiological models, SEIR disease model, bifurcation, chaotic behavior, 0-1 test

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Authors: Qian Li, Zhaoping Zhong

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Sewage sludge, a typical solid waste, has inevitably been produced in enormous quantities in China. Still worse, the amount of sewage sludge produced has been increasing due to rapid economic development and urbanization. Compared to the conventional method to treat sewage sludge, pyrolysis has been considered an economic and ecological technology because it can significantly reduce the sludge volume, completely kill pathogens, and produce valuable solid, gas, and liquid products. However, the large-scale utilization of sludge biochar has been limited due to the considerable risk posed by heavy metals in the sludge. Heavy metals enriched in pyrolytic biochar could be divided into exchangeable, reducible, oxidizable, and residual forms. The residual form of heavy metals is the most stable and cannot be used by organisms. Kaolin and zeolite are environmentally friendly inorganic minerals with a high surface area and heat resistance characteristics. So, they exhibit the enormous potential to immobilize heavy metals. In order to reduce the risk of leaching heavy metals in the pyrolysis biochar, this study pyrolyzed sewage sludge mixed with kaolin/zeolite in a small rotary kiln. The influences of additives and pyrolysis temperature on the leaching concentration and morphological transformation of heavy metals in pyrolysis biochar were investigated. The potential mechanism of stabilizing heavy metals in the co-pyrolysis of sludge blended with kaolin/zeolite was explained by scanning electron microscopy, X-ray diffraction, and specific surface area and porosity analysis. The European Community Bureau of Reference sequential extraction procedure has been applied to analyze the forms of heavy metals in sludge and pyrolysis biochar. All the concentrations of heavy metals were examined by flame atomic absorption spectrophotometry. Compared with the proportions of heavy metals associated with the F4 fraction in pyrolytic carbon prepared without additional agents, those in carbon obtained by co-pyrolysis of sludge and kaolin/zeolite increased. Increasing the additive dosage could improve the proportions of the stable fraction of various heavy metals in biochar. Kaolin exhibited a better effect on stabilizing heavy metals than zeolite. Aluminosilicate additives with excellent adsorption performance could capture more released heavy metals during sludge pyrolysis. Then heavy metal ions would react with the oxygen ions of additives to form silicate and aluminate, causing the conversion of heavy metals from unstable fractions (sulfate, chloride, etc.) to stable fractions (silicate, aluminate, etc.). This study reveals that the efficiency of stabilizing heavy metals depends on the formation of stable mineral compounds containing heavy metals in pyrolysis biochar.

Keywords: co-pyrolysis, heavy metals, immobilization mechanism, sewage sludge

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Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

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Authors: Ana Maria Reis D'Azevedo Breda, Catarina Maria Neto da Cruz

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The Japanese art of origami provides a rich context for designing exploratory mathematical activities for children and young people. By folding a simple sheet of paper, fascinating and surprising planar and spatial configurations emerge. Equally surprising is the unfolding process, which also produces striking patterns. The procedure of folding, unfolding, and folding again allows the exploration of interesting geometric patterns. When adequately and systematically done, we may deduce some of the mathematical rules ruling origami. As the child/youth folds the sheet of paper repeatedly, he can physically observe how the forms he obtains are transformed and how they relate to the pattern of the corresponding unfolding, creating space for the understanding/discovery of mathematical principles regulating the folding-unfolding process. As part of a 2023 Summer Academy organized by a Portuguese university, a session entitled “Folding, Thinking and Generalizing” took place. Twenty-three students attended the session, all enrolled in the 2nd cycle of Portuguese Basic Education and aged between 10 and 12 years old. The main focus of this session was to foster the development of critical cognitive and socio-emotional skills among these young learners using origami. These skills included creativity, critical analysis, mathematical reasoning, collaboration, and communication. Employing a qualitative, descriptive, and interpretative analysis of data collected during the session through field notes and students’ written productions, our findings reveal that structured origami-based activities not only promote student engagement with mathematical concepts in a playful and interactive but also facilitate the development of socio-emotional skills, which include collaboration and effective communication between participants. This research highlights the value of integrating origami into educational practices, highlighting its role in supporting comprehensive cognitive and emotional learning experiences.

Keywords: skills, origami rules, active learning, hands-on activities

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Authors: Kwon Eunhee, Park Dongcheon, Jung Jaemin

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In countries around the world, environmental regulations are being strengthened, and Korea is no exception to this trend, which means that environment pollution and the environmental load have recently become a significant issue. For this reason, in this study limestone was replaced with cementitious powder to reduce the volume of construction waste as well as the emission of carbon dioxide caused by Tal-carbonate reaction. The research found that cementitious powder can be used as a substitute for limestone. However, the mix proportions of fine aggregate and powder included in the cementitious powder appear to have a great effect on substitution. Thus, future research should focus on developing a technology that can effectively separate and discharge fine aggregate and powder in the cementitious powder.

Keywords: waste cementitious powder, fine aggregate powder, CO2 emission, decarbonation reaction, calcining process

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Authors: Abdullahi Mohammed Auwal

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Formation and change or decamping from one political party to another have now become a common trend in Nigeria. Many of the parties’ members who could not secure positions and or win elections in their parties or are not very much satisfied with the trends occurring in the party’s internal democratic principles and mechanisms, change their respective parties. This paper developed/presented and analyzed the used of non linear mathematical model for defections between two political parties using epidemiological approach. The whole population was assumed to be a constant and homogeneously mixed. Equilibria have been analytically obtained and their local and global stability discussed. Conditions for the co-existence of both the political parties have been determined, in the study of defections between People Democratic Party (PDP) and All Progressive Congress (APC) in Nigeria using numerical simulations to support the analytical results.

Keywords: model, political parties, deffection, stability, equilibrium, epidemiology

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Authors: M. Ziółkowska, J. T. Duda, J. Milewska-Duda

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This paper describes an approach to the adsorption phenomena modeling aimed at specifying the adsorption mechanisms on localized or nonlocalized adsorbent sites, when applied to the nanocarbons. The concept comes from the fundamental thermodynamic description of adsorption equilibrium and is based on numerical calculations of the hydrogen adsorbed particles volume on the surface of selected nanocarbons: single-walled nanotube and nanocone. This approach enables to obtain information on adsorption mechanism and then as a consequence to take appropriate mathematical adsorption model, thus allowing for a more reliable identification of the material porous structure. Theoretical basis of the approach is discussed and newly derived results of the numerical calculations are presented for the selected nanocarbons.

Keywords: adsorption, mathematical modeling, nanocarbons, numerical analysis

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: gravity gradient, gravity gradient sensor, accelerometer, single-axis rotation modulation

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Authors: Otgonjargal Damdinbaljir

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Background: Infant feeding practices have a major role in determining the nutritional status of children and are associated with household socioeconomic and demographic factors. In 2010, Mongolia used WHO 2008 edition of Indicators for assessing infant and young child feeding practices for the first time. Objective: To evaluate the feeding status of infants and young children under 2 years old in Mongolia. Materials and Methods: The study was conducted by cluster random sampling. The data on breastfeeding and complementary food supplement of the 350 infants and young children aged 0-23 months in 21 provinces of the 4 economic regions of the country and capital Ulaanbaatar city were collected through questionnaires. The feeding status was analyzed according to the WHO 2008 edition of Indicators for assessing infant and young child feeding practices. Analysis of data: Survey data was analysed using the PASW statistics 18.0 and EPI INFO 2000 software. For calculation of overall measures for the entire survey sample, analyses were stratified by region. Age-specific feeding patterns were described using frequencies, proportions and survival analysis. Logistic regression was done with feeding practice as dependent and socio demographic factors as independent variables. Simple proportions were calculated for each IYCF indicator. The differences in the feeding practices between sexes and age-groups, if any, were noted using chi-square test. Ethics: The Ethics Committee under the auspices of the Ministry of Health approved the study. Results: A total of 350 children aged 0-23 months were investigated. The rate of ever breastfeeding of children aged 0-23 months reached up to 98.2%, while the percentage of early initiation of breastfeeding was only 85.5%. The rates of exclusive breastfeeding under 6 months, continued breastfeeding for 1 year, and continued breastfeeding for 2 years were 71.3%, 74% and 54.6%, respectively. The median time of giving complementary food was the 6th month and the weaning time was the 9th month. The rate of complementary food supplemented from 6th-8th month in time was 80.3%. The rates of minimum dietary diversity, minimum meal frequency, and consumption of iron-rich or iron-fortified foods among children aged 6-23 months were 52.1%, 80.8% (663/813) and 30.1%, respectively. Conclusions: The main problems revealed from the study were inadequate category and frequency of complementary food, and the low rate of consumption of iron-rich or iron-fortified foods were the main issues to be concerned on infant feeding in Mongolia. Our findings have highlighted the need to encourage mothers to enrich their traditional wheat- based complementary foods add more animal source foods and vegetables.

Keywords: complementary feeding, early initiation of breastfeeding, exclusive breastfeeding, minimum meal frequency

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Authors: Nicolás Clavijo Buriticá, Laura Viviana Triana Sanchez

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This research develops a productive context associated with the aquaculture industry in northern Tolima-Colombia, specifically in the town of Lerida. Strategic aspects of chain of fish Production-Distribution, especially those related to supply network design of an association devoted to cultivating, farming, processing and marketing of fish are addressed. This research is addressed from a special approach of Supply Chain Management (SCM) which guides management objectives to the system sustainability; this approach is called Sustainable Supply Chain Management (SSCM). The network design of fish production-distribution system is obtained for the case study by two mathematical programming models that aims to maximize the economic benefits of the chain and minimize total supply chain costs, taking into account restrictions to protect the environment and its implications on system productivity. The results of the mathematical models validated in the productive situation of the partnership under study, called Asopiscinorte shows the variation in the number of open or closed locations in the supply network that determines the final network configuration. This proposed result generates for the case study an increase of 31.5% in the partial productivity of storage and processing, in addition to possible favorable long-term implications, such as attending an agile or not a consumer area, increase or not the level of sales in several areas, to meet in quantity, time and cost of work in progress and finished goods to various actors in the chain.

Keywords: Sustainable Supply Chain, mathematical programming, aquaculture industry, Supply Chain Design, Supply Chain Configuration

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Authors: Dalita G. S. M. Cavalcante, Elton A. P. dos Reis, Andressa S. Gomes, Caroline S. Danna, Leandra Ernest Kerche-Silva, Eidi Yoshihara, Aldo E. Job

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In order to minimize environmental impacts, a composite was developed from mixture of leather shavings (LE) with natural rubber (NR), which patent is already deposited. The new material created can be used in applications such as floors e heels for shoes. Besides these applications, the aim is to use this new material for the production of products for the textile industry, such as boots, gloves and bags. But the question arises, as to biocompatibility of this new material. This is justified because the structure of the leather shavings has chrome. The trivalent chromium is usually not toxic, but the hexavalent chromium can be highly toxic and genotoxic for living beings, causing damage to the DNA molecule and contributing to the formation of cancer. Based on this, the objective of this study is evaluate the possible genotoxic effects of the new composite, using as system - test two cell lines (MRC-5 and CHO-K1) by comet assay. For this, the production of the composite was performed in three proportions: for every 100 grams of NR was added 40 (E40), 50 (E50) or 60 (E60) grams of LE. The latex was collected from the rubber tree (Hevea brasiliensis). For vulcanization of the NR, activators and accelerators were used. The two cell lines were exposed to the new composite in its three proportions using elution method, that is, cells exposed to liquid extracts obtained from the composite for 24 hours. For obtaining the liquid extract, each sample of the composite was crushed into pieces and mixed with an extraction solution. The quantification of total chromium and hexavalent chromium in the extracts were performed by Optical Emission Spectrometry by Inductively Coupled Plasma (ICP-OES). The levels of DNA damage in cells exposed to both extracts were monitored by alkaline version of the comet assay. The results of the quantification of metals in ICP-OES indicated the presence of total chromium in different extracts, but were not detected presence of hexavalent chromium in any extract. Through the comet assay were not found DNA damage of the CHO-K1 cells exposed to both extracts. As for MRC-5, was found a significant increase in DNA damage in cells exposed to E50 and E60. Based on the above data, it can be asserted that the extracts obtained from the composite were highly genotoxic for MRC-5 cells. These biological responses do not appear to be related to chromium metal, since there was a predominance of trivalent chromium in the extracts, indicating that during the production process of the new composite, there was no formation of hexavalent chromium. In conclusion it can infer that the leather shavings containing chromium can be reused, thereby reducing the environmental impacts of this waste. Already on the composite indicates to its incorporation in applications that do not aim at direct contact with the human skin, and it is suggested the chain of composite production be studied, in an attempt to make it biocompatible so that it may be safely used by the textile industry.

Keywords: cell line, chrome, genotoxicity, leather, natural rubber

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Authors: Gak-Gyu Kim, Won Il Jung

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According to a remarkable development of science and technology, function and role of the system of engineering fields has recently been diversified. The system has become increasingly more complex and precise, and thus, system designers intended to maximize reliability concentrate more effort at the design stage. This study deals with the reliability redundancy optimization problem (RROP) for k-out-of-n: G system configuration with cold standby and warm standby components. This paper further intends to present the optimal mathematical model through which the following three elements of (i) multiple components choices, (ii) redundant components quantity and (iii) the choice of redundancy strategies may be combined in order to maximize the reliability of the system. Therefore, we focus on the following three issues. First, we consider RROP that there exists warm standby state as well as cold standby state of the component. Second, as eliminating an approximation approach of the previous RROP studies, we construct a precise model for system reliability. Third, given transition time when the state of components changes, we present not simply a workable solution but the advanced method. For the wide applicability of RROPs, moreover, we use absorbing continuous time Markov chain and matrix analytic methods in the suggested mathematical model.

Keywords: RROP, matrix analytic methods, k-out-of-n: G system, MTTF, absorbing continuous time Markov Chain

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Authors: Butchi Kameswara Rao Chittem, Rooban Kumar

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Cement concrete is a complex mixture of different materials. Concrete is believed to have a good fire resistance. Behaviour of concrete depends on its mix proportions and its constituent materials when it is subjected to elevated temperatures. Loss in compressive strength, loss in weight or mass, change in colour and spall of concrete are reported in literature as effects of elevated temperature on concrete. In this paper results are reported on the behaviour of normal strength concrete and high strength concrete subjected to temperatures 200°C, 400°C, 600°C, and 800°C and different cooling regimes viz. air cooling, water quenching. Rebound hammer test was also conducted to study the changes in surface hardness of concrete specimens subjected to elevated temperatures.

Keywords: normal strength concrete, high-strength concrete, temperature, NDT

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Authors: Yuan-Jye Tseng, Yi-Shiuan Chen

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The paper presented a sustainable design model for integrated evaluation of the design and supply chain of a product for the sustainable objectives. To design a product, there can be alternative ways to assign the detailed specifications to fulfill the same design objectives. In the design alternative cases, different material and manufacturing processes with various supply chain activities may be required for the production. Therefore, it is required to evaluate the different design cases based on the sustainable objectives. In this research, a closed-loop design model is developed by integrating the forward design model and reverse design model. From the supply chain point of view, the decisions in the forward design model are connected with the forward supply chain. The decisions in the reverse design model are connected with the reverse supply chain considering the sustainable objectives. The purpose of this research is to develop a mathematical model for analyzing the design cases by integrated evaluating the criteria in the closed-loop design and the closed-loop supply chain. The decision variables are built to represent the design cases of the forward design and reverse design. The cost parameters in a forward design include the costs of material and manufacturing processes. The cost parameters in a reverse design include the costs of recycling, disassembly, reusing, remanufacturing, and disposing. The mathematical model is formulated to minimize the total cost under the design constraints. In practical applications, the decisions of the mathematical model can be used for selecting a design case for the purpose of sustainable design of a product. An example product is demonstrated in the paper. The test result shows that the sustainable design model is useful for integrated evaluation of the design and the supply chain to achieve the sustainable objectives.

Keywords: closed-loop design, closed-loop supply chain, design evaluation, supply chain management, sustainable design model

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Authors: Cristian Patrascioiu, Loredana Negoita

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This paper is focused on modeling and simulation of the tubular heaters. The paper is structured in four parts: the structure of the tubular convection section, the heat transfer model, the adaptation of the mathematical model and the solving model. The main hypothesis of the heat transfer modeling is that the heat exchanger of the convective tubular heater is a lumped system. In the same time, the model uses the heat balance relations, Newton’s law and criteria relations. The numerical program achieved allows for the estimation of the burn gases outlet temperature and the heated flow outlet temperature.

Keywords: heat exchanger, mathematical modelling, nonlinear equation system, Newton-Raphson algorithm

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Authors: Gurmeet Singh Cheema, Gurjinder Singh, Amardeep Singh Kang

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Aluminium alloy 6061 is a medium to high strength heat-treatable alloy which has very good corrosion resistance and very good weldability. Friction Stir Welding was developed and this technique has attracted considerable interest from the aerospace and automotive industries since it is able to produce defect free joints particularly for light metals i.e aluminum alloy and magnesium alloy. In the friction stir welding process, welding parameters such as tool rotational speed, welding speed and tool shoulder diameter play a major role in deciding the weld quality. In this research work, an attempt has been made to understand the effect of tool rotational speed, welding speed and tool shoulder diameter on friction stir welded AA6061 aluminium alloy joints. Statistical tool such as central composite design is used to develop the mathematical relationships. The mathematical model was developed to predict mechanical properties of friction stir welded aluminium alloy joints at the 95% confidence level.

Keywords: aluminium alloy, friction stir welding, central composite design, mathematical relationship

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Authors: Jean Paul Muambangu Milambo, Peter Nyasulu, John Akudugu, Leonidas Ndayisaba, Joyce Tsoka-Gwegweni, Lebwaze Massamba Bienvenu, Mitshindo Mwambangu Chiro

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In 2018, non-communicable diseases (NCDs) were responsible for 48% of deaths in the Democratic Republic of Congo (DRC), with cancer contributing to 5% of these deaths. There is a notable absence of cancer registries, capacity-building activities, budgets, and treatment roadmaps in the DRC. Current cancer estimates are primarily based on mathematical modeling with limited data from neighboring countries. This study aimed to assess cancer subtype prevalence in Kinshasa hospitals and compare these findings with WHO model estimates. Methods: A retrospective observational study was conducted from 2018 to 2020 at HJ Hospitals in Kinshasa. Data were collected using American Cancer Society (ACS) questionnaires and physician logs. Descriptive analysis was performed using STATA version 16 to estimate cancer burden and provide evidence-based recommendations. Results: The results from the chart review at HJ Hospitals in Kinshasa (2018-2020) indicate that out of 6,852 samples, approximately 11.16% were diagnosed with cancer. The distribution of cancer subtypes in this cohort was as follows: breast cancer (33.6%), prostate cancer (21.8%), colorectal cancer (9.6%), lymphoma (4.6%), and cervical cancer (4.4%). These figures are based on histopathological confirmation at the facility and may not fully represent the broader population due to potential selection biases related to geographic and financial accessibility to the hospital. In contrast, the World Health Organization (WHO) model estimates for cancer prevalence in the DRC show different proportions. According to WHO data, the distribution of cancer types is as follows: cervical cancer (15.9%), prostate cancer (15.3%), breast cancer (14.9%), liver cancer (6.8%), colorectal cancer (5.9%), and other cancers (41.2%) (WHO, 2020). Conclusion: The data indicate a rising cancer prevalence in DRC but highlight significant gaps in clinical, biomedical, and genetic cancer data. The establishment of a population-based cancer registry (PBCR) and a defined cancer management pathway is crucial. The current estimates are limited due to data scarcity and inconsistencies in clinical practices. There is an urgent need for multidisciplinary cancer management, integration of palliative care, and improvement in care quality based on evidence-based measures.

Keywords: cancer, risk factors, DRC, gene-environment interactions, survivors

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Authors: Jacob A. Braun

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This paper uses mathematical modeling to show the spread of Herpes Simplex type-2 with and without the usage of condoms in a college population. The model uses four differential equations to calculate the data for the simulation. The dt increment used is one week. It also runs based on a fixated period. The period chosen was five years to represent time spent in college. The average age of the individual is 21, once again to represent the age of someone in college. In the total population, there are almost two times as many women who have Herpes Simplex Type-2 as men. Additionally, Herpes Simplex Type-2 does not have a known cure. The goal of the model is to show how condom usage affects women’s chances of receiving the virus in the hope of being able to reduce the number of women infected. In the end, the model demonstrates that condoms offer significant protection to women from the virus. Since fewer women are infected with the virus when condoms are used, in turn, fewer males are infected. Since Herpes Simplex Type-2 affects the carrier for their whole life, a small decrease of infections could lead to large ramifications over time. Specifically, a small decrease of infections at a young age, such as college, could have a very big effect on the long-term number of people infected with the virus.

Keywords: college, condom, Herpes, mathematical modelling

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Authors: Marlone D. Severo

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A pre- and post-test quasi-experimental design was used to test the intervention of Trachtenberg Speed Math on the mathematical competency of sixty (60) matched-paired students with a poor performing grade in Mathematics from one of the biggest public national high school at the South of Metro Manila. Both control and experimental group were administered with the Attitude Towards Mathematics Inventory (ATMI) before the pretest were given and both group showed high dislike for Mathematics. Pretest showed a 53 percent accuracy for the control group and 51 percent for the experimental group using a 15-item long multiplication test without any aid of a computing device. The experimental group were taught how to use the Trachtenberg number-keys and techniques in multiplication between October 2014 to March 2015. Post-test showed an improvement in the experimental group with 96 percent accuracy for the control group and a dismal 57 percent for the control group in long-multiplication. Post-test ATMI were administered. The control group showed a great dislike towards Mathematics, while the experimental group showed a positive attitude towards the subject.

Keywords: attitude towards mathematics, mathematical competency, number-keys, trachtenberg speed math

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Authors: Beata Jackowska-Zduniak

Abstract:

We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: mathematical modeling, ordinary differential equations, endocrine system, delay differential equation

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Authors: Ofosuhene O. Apenteng, Noor Azina Ismail

Abstract:

Recently tourism is a major foreign exchange earner in the World. In this paper, we propose the mathematical model to study the impact of tourists on the spread of HIV incidences using compartmental differential equation models. Simulation studies of reproduction number are used to demonstrate new insights on the spread of HIV disease. The periodogram analysis of a time series was used to determine the speed at which the disease is spread. The results indicate that with the persistent flow of tourism into a country, the disease status has increased the epidemic rate. The result suggests that the government must put more control on illegal prostitution, unprotected sexual activity as well as to emphasis on prevention policies that include the safe sexual activity through the campaign by the tourism board.

Keywords: HIV/AIDS, mathematical transmission modeling, tourists, stability, simulation

Procedia PDF Downloads 391

Authors: Hanbey Hazar

Abstract:

An experimental study is conducted to evaluate the effects of using blends of diesel fuel with dimethyl adipate (DMA) in proportions of 2%, 6/%, and 12% on a coated engine. In this study, cylinder, piston, exhaust and inlet valves which are combustion chamber components have been coated with a ceramic material. Cylinder, exhaust and inlet valves of the diesel engine used in the tests were coated with ekabor-2 commercial powder, which is a ceramic material, to a thickness of 50 µm, by using the boriding method. The piston of a diesel engine was coated in 300 µm thickness with bor-based powder by using plasma coating method. Due to thermal barrier coating, the diesel engine's hazardous emission values decreased.

Keywords: diesel engine, dimethyl adipate (DMA), exhaust emissions, coating

Procedia PDF Downloads 273