Search results for: Mathematical modelling

Authors: Lee Bih Ni, Nurul Asyikin Binti Hassan

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This paper discusses the use of mnemonic and mathematical methods in enhancing the understanding of history. Mnemonics can help students from all levels including high school and in various disciplines including language, math and history. At the secondary level, students are exposed to various courses that require them to remember many facts that can be mastered through the application of mnemonic techniques. Researchers use narrative literature studies to illustrate the current state of art and science in the field of research focused. Researchers used narrative literature reviews to build a scientific base of knowledge. Researchers gather all the key points in the discussion, and put it here by referring to the specific field where the paper is essentially based. The findings suggest that the use of mnemonic techniques can improve the individual's memory by adding little effort. In implementing mnemonic techniques, it is important to integrate mathematics and history in the course as both are interconnected as mathematics has shaped our history and vice versa. This study shows that memory skills can actually be improved; the human mind can remember something more than expected.

Keywords: Cognitive strategy, mnemonic technique, secondary school level study, mathematical mnemonic.

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Authors: Jahedul Islam Chowdhury, Bao Kha Nguyen, David Thornhill, Roy Douglas, Stephen Glover

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Organic Rankine Cycle (ORC) is the most commonly used method for recovering energy from small sources of heat. The investigation of the ORC in supercritical condition is a new research area as it has a potential to generate high power and thermal efficiency in a waste heat recovery system. This paper presents a steady state ORC model in supercritical condition and its simulations with a real engine’s exhaust data. The key component of ORC, evaporator, is modelled using finite volume method, modelling of all other components of the waste heat recovery system such as pump, expander and condenser are also presented. The aim of this paper is to investigate the effects of mass flow rate and evaporator outlet temperature on the efficiency of the waste heat recovery process. Additionally, the necessity of maintaining an optimum evaporator outlet temperature is also investigated. Simulation results show that modification of mass flow rate is the key to changing the operating temperature at the evaporator outlet.

Keywords: Organic Rankine cycle, supercritical condition, steady state model, waste heat recovery.

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Authors: Leo Laine, Morgan Johansson

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To meet the civilizations future needs for safe living and low environmental footprint, the engineers designing the complex systems of tomorrow will need efficient ways to model and optimize these systems for their intended purpose. For example, a civil defence shelter and its subsystem components needs to withstand, e.g. airblast and ground shock from decided design level explosion which detonates with a certain distance from the structure. In addition, the complex civil defence shelter needs to have functioning air filter systems to protect from toxic gases and provide clean air, clean water, heat, and electricity needs to also be available through shock and vibration safe fixtures and connections. Similar complex building systems can be found in any concentrated living or office area. In this paper, the authors use a multidomain modelling language called Modelica to model a concrete wall as a single degree of freedom (SDOF) system with elastoplastic properties with the implemented option of plastic hardening. The elastoplastic model was developed and implemented in the open source tool OpenModelica. The simulation model was tested on the case with a transient equivalent reflected pressure time history representing an airblast from 100 kg TNT detonating 15 meters from the wall. The concrete wall is approximately regarded as a concrete strip of 1.0 m width. This load represents a realistic threat on any building in a city like area. The OpenModelica model results were compared with an Excel implementation of a SDOF model with an elastic-plastic spring using simple fixed timestep central difference solver. The structural displacement results agreed very well with each other when it comes to plastic displacement magnitude, elastic oscillation displacement, and response times.

Keywords: Airblast from explosives, elastoplastic spring model, Modelica modelling language, SDOF, structural response of concrete structure.

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Authors: Usman Ali Khan, Bismah Tariq, Khalida Raza, Saima Malik, Aoun Muhammad

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This research paper is based upon the simulation of gradient of mathematical functions and scalar fields using MATLAB. Scalar fields, their gradient, contours and mesh/surfaces are simulated using different related MATLAB tools and commands for convenient presentation and understanding. Different mathematical functions and scalar fields are examined here by taking their gradient, visualizing results in 3D with different color shadings and using other necessary relevant commands. In this way the outputs of required functions help us to analyze and understand in a better way as compared to just theoretical study of gradient.

Keywords: MATLAB, Gradient, Contour, Scalar Field, Mesh

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Authors: T. K. Sriram, Joydip Dhar

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Models based on stage structure have found varied applications in population models. This paper proposes a stage structured model to study the trends in the computer and video game playing population of US. The game paying population is divided into three compartments based on their age group. After simulating the mathematical model, a forecast of the number of game players in each stage as well as an approximation of the average age of game players in future has been made.

Keywords: Age structure, Forecasting, Mathematical modeling, Stage structure.

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Authors: Serkan Narli

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This study aims to specify to what extent students understand topology during the lesson and to determine possible misconceptions. 14 teacher trainees registered at Secondary School Mathematics education department were observed in the topology lessons throughout a semester and data collected at the first topology lesson is presented here. Students- knowledge was evaluated using a written test right before and after the topology lesson. Thus, what the students learnt in terms of the definition and examples of topologic space were specified as well as possible misconceptions. The findings indicated that students did not fully comprehend the topic and misunderstandings were due to insufficient pre-requisite knowledge of abstract mathematical topics and mathematical notation.

Keywords: Mathematics Education, Teacher Education, Topology.

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Authors: Olivia A. Wilson, Hannah E. Power, Murray Kendall

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Sydney Harbour is an iconic location with a dense population and low-lying development. On the east coast of Australia, facing the Pacific Ocean, it is exposed to several tsunamigenic trenches. This paper presents a component of the most detailed assessment of the potential for earthquake-generated tsunami impact on Sydney Harbour to date. Models in this study use dynamic tides to account for tide-tsunami interaction. Sydney Harbour’s tidal range is 1.5 m, and the spring tides from January 2015 that are used in the modelling for this study are close to the full tidal range. The tsunami wave trains modelled include hypothetical tsunami generated from earthquakes of magnitude 7.5, 8.0, 8.5, and 9.0 M_W from the Puysegur and New Hebrides trenches as well as representations of the historical 1960 Chilean and 2011 Tohoku events. All wave trains are modelled for the peak wave to coincide with both a low tide and a high tide. A single wave train, representing a 9.0 M_W earthquake at the Puysegur trench, is modelled for peak waves to coincide with every hour across a 12-hour tidal phase. Using the hydrodynamic model ANUGA, results are compared according to the impact parameters of inundation area, depth variation and current speeds. Results show that both maximum inundation area and depth variation are tide dependent. Maximum inundation area increases when coincident with a higher tide, however, hazardous inundation is only observed for the larger waves modelled: NH90high and P90high. The maximum and minimum depths are deeper on higher tides and shallower on lower tides. The difference between maximum and minimum depths varies across different tidal phases although the differences are slight. Maximum current speeds are shown to be a significant hazard for Sydney Harbour; however, they do not show consistent patterns according to tide-tsunami phasing. The maximum current speed hazard is shown to be greater in specific locations such as Spit Bridge, a narrow channel with extensive marine infrastructure. The results presented for Sydney Harbour are novel, and the conclusions are consistent with previous modelling efforts in the greater area. It is shown that tide must be a consideration for both tsunami modelling and emergency management planning. Modelling with peak tsunami waves coinciding with a high tide would be a conservative approach; however, it must be considered that maximum current speeds may be higher on other tides.

Keywords: Emergency management, Sydney, tide-tsunami interaction, tsunami impact.

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Authors: M. K. Balyan

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The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: Dynamical diffraction, hologram, object image, X-ray holography.

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Authors: Tofigh Hamidavi, Sepehr Abrishami, Pasquale Ponterosso, David Begg

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Structural design and analysis is an important and time-consuming process, particularly at the conceptual design stage. Decisions made at this stage can have an enormous effect on the entire project, as it becomes ever costlier and more difficult to alter the choices made early on in the construction process. Hence, optimisation of the early stages of structural design can provide important efficiencies in terms of cost and time. This paper suggests a structural design optimisation (SDO) framework in which Genetic Algorithms (GAs) may be used to semi-automate the production and optimisation of early structural design alternatives. This framework has the potential to leverage conceptual structural design innovation in Architecture, Engineering and Construction (AEC) projects. Moreover, this framework improves the collaboration between the architectural stage and the structural stage. It will be shown that this SDO framework can make this achievable by generating the structural model based on the extracted data from the architectural model. At the moment, the proposed SDO framework is in the process of validation, involving the distribution of an online questionnaire among structural engineers in the UK.

Keywords: Building Information Modelling, BIM, Genetic Algorithm, GA, architecture-engineering-construction, AEC, Optimisation, structure, design, population, generation, selection, mutation, crossover, offspring.

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Authors: Cheng Zhang, James Marco, Walid Allafi, Truong Q. Dinh, W. D. Widanage

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Equivalent circuit models (ECMs) are widely used in battery management systems in electric vehicles and other battery energy storage systems. The battery dynamics and the model parameters vary under different working conditions, such as different temperature and state of charge (SOC) levels, and therefore online parameter identification can improve the modelling accuracy. This paper presents a way of online ECM parameter identification using a continuous time (CT) estimation method. The CT estimation method has several advantages over discrete time (DT) estimation methods for ECM parameter identification due to the widely separated battery dynamic modes and fast sampling. The presented method can be used for online SOC estimation. Test data are collected using a lithium ion cell, and the experimental results show that the presented CT method achieves better modelling accuracy compared with the conventional DT recursive least square method. The effectiveness of the presented method for online SOC estimation is also verified on test data.

Keywords: Equivalent circuit model, continuous time domain estimation, linear integral filter method, parameter and SOC estimation, recursive least square.

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Authors: Emmanuel Agunloye, Asterios Gavriilidis, Luca Mazzei

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Gold nanoparticles are commonly synthesized by reducing chloroauric acid with sodium citrate. This method, referred to as the citrate method, can produce spherical gold nanoparticles (NPs) in the size range 10-150 nm. Gold NPs of this size are useful in many applications. However, the NPs are usually polydisperse and irreproducible. A better understanding of the synthesis mechanisms is thus required. This work thoroughly investigated the only model that describes the synthesis. This model combines mass and population balance equations, describing the NPs synthesis through a sequence of chemical reactions. Chloroauric acid reacts with sodium citrate to form aurous chloride and dicarboxy acetone. The latter organizes aurous chloride in a nucleation step and concurrently degrades into acetone. The unconsumed precursor then grows the formed nuclei. However, depending on the pH, both the precursor and the reducing agent react differently thus affecting the synthesis. In this work, we investigated the model for different conditions of pH, temperature and initial reactant concentrations. To solve the model, we used Parsival, a commercial numerical code, whilst to test it, we considered various conditions studied experimentally by different researchers, for which results are available in the literature. The model poorly predicted the experimental data. We believe that this is because the model does not account for the acid-base properties of both chloroauric acid and sodium citrate.

Keywords: Gold nanoparticles, Citrate method, Turkevich organizer theory, population balance modelling.

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Authors: N. Outili, A-H. Meniai

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Modeling transfer phenomena in several chemical engineering operations leads to the resolution of partial differential equations systems. According to the complexity of the operations mechanisms, the equations present a nonlinear form and analytical solution became difficult, we have then to use numerical methods which are based on approximations in order to transform a differential system to an algebraic one.Finite element method is one of numerical methods which can be used to obtain an accurate solution in many complex cases of chemical engineering.The packed columns find a large application like contactor for liquid-liquid systems such solvent extraction. In the literature, the modeling of this type of equipment received less attention in comparison with the plate columns.A mathematical bidimensionnal model with radial and axial dispersion, simulating packed tower extraction behavior was developed and a partial differential equation was solved using the finite element method by adopting the Galerkine model. We developed a Mathcad program, which can be used for a similar equations and concentration profiles are obtained along the column. The influence of radial dispersion was prooved and it can-t be neglected, the results were compared with experimental concentration at the top of the column in the extraction system: acetone/toluene/water.

Keywords: finite element method, Galerkine method, liquidliquid extraction modelling, packed column simulation, two dimensional model

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Authors: Farzad Khajavi, Farzaneh Jalilfar, Faranak Jafari, Leila Shokrani

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Formulation of gliclazide in the form of extended-release tablet in 30 and 60 mg dosage forms was performed using hypromellose (HPMC K4M) as a retarding agent. Drug-release profiles were investigated in comparison with references Diamicron MR 30 and 60 mg tablets. The effect of size of powder particles, the amount of hypromellose in formulation, hardness of tablets, and also the effect of halving the tablets were investigated on drug release profile. A mathematical model which describes hypromellose behavior in initial times of drug release was proposed for the estimation of hypromellose content in modified-release gliclazide 60 mg tablet. This model is based on erosion of hypromellose in dissolution media. The model is applicable to describe release profiles of insoluble drugs. Therefore, by using dissolved amount of drug in initial times of dissolution and the model, the amount of hypromellose in formulation can be predictable. The model was used to predict the HPMC K4M content in modified-release gliclazide 30 mg and extended-release quetiapine 200 mg tablets.

Keywords: Hypromellose, gliclazide, drug release, modified-release tablet, mathematical model.

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Authors: Liliana M. Marinelli, Cristina T. Varanese

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In the last few years, students from higher education have difficulties in grasping mathematical concepts which support physical matters, especially those in the first years of this education. Classical Physics teaching turns to be complex when students are not able to make use of mathematical tools which lead to the conceptual structure of Physics. When derivation and integration rules are not used or developed in parallel with other disciplines, the physical meaning that we attempt to convey turns to be complicated. Due to this fact, it could be of great use to see the Classical Mechanics from an axiomatic approach, where the correspondence rules give physical meaning, if we expect students to understand concepts clearly and accurately. Using the Minkowski point of view adapted to a two-dimensional space and time where vectors, matrices, and straight lines (worked from an affine space) give mathematical and physical rigorosity even when it is more abstract. An interesting option would be to develop the disciplinary contents from an axiomatic version which embraces the Classical Mechanics as a particular case of Relativistic Mechanics. The observation about the increase in the difficulties stated by students in the first years of education allows this idea to grow as a possible option to improve performance and understanding of the concepts of this subject.

Keywords: Axiom, classical physics, physical concepts, relativity.

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Authors: Takuya Sumi, Syoko Nukaya, Takashi Kaburagi, Hiroshi Tanaka, Kajiro Watanabe, Yosuke Kurihara

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We propose an unconstrained measurement system for scratching motion based on mathematical model of unconstrained bed sensing method which could measure the bed vibrations due to the motion of the person on the bed. In this paper, we construct mathematical model of the unconstrained bed monitoring system; and we apply the unconstrained bed sensing method to the system for detecting scratching motion. The proposed sensors are placed under the three bed feet. When the person is lying on the bed, the output signals from the sensors are proportional to the magnitude of the vibration due to the scratching motion. Hence, we could detect the subject’s scratching motion from the output signals from ceramic sensors. We evaluated two scratching motions using the proposed system in the validity experiment as follows: 1st experiment is the subject’s scratching the right side cheek with his right hand, and; 2nd experiment is the subject’s scratching the shin with another foot. As the results of the experiment, we recognized the scratching signals that enable the determination when the scratching occurred. Furthermore, the difference among the amplitudes of the output signals enabled us to estimate where the subject scratched.

Keywords: Unconstrained bed sensing method, scratching, body movement, itchy, piezoceramics.

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Authors: Karim Hamidi Machekposhti, Hossein Sedghi, Abdolrasoul Telvari, Hossein Babazadeh

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Floods have huge environmental and economic impact. Therefore, flood prediction is given a lot of attention due to its importance. This study analysed the annual maximum streamflow (discharge) (AMS or AMD) of Karkheh River in Karkheh River Basin for flood predicting using ARIMA model. For this purpose, we use the Box-Jenkins approach, which contains four-stage method model identification, parameter estimation, diagnostic checking and forecasting (predicting). The main tool used in ARIMA modelling was the SAS and SPSS software. Model identification was done by visual inspection on the ACF and PACF. SAS software computed the model parameters using the ML, CLS and ULS methods. The diagnostic checking tests, AIC criterion, RACF graph and RPACF graphs, were used for selected model verification. In this study, the best ARIMA models for Annual Maximum Discharge (AMD) time series was (4,1,1) with their AIC value of 88.87. The RACF and RPACF showed residuals’ independence. To forecast AMD for 10 future years, this model showed the ability of the model to predict floods of the river under study in the Karkheh River Basin. Model accuracy was checked by comparing the predicted and observation series by using coefficient of determination (R²).

Keywords: Time series modelling, stochastic processes, ARIMA model, Karkheh River.

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Authors: Mohammed Salahat, Steve Wade

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This paper presents and compares the SSDDD “Systematic Soft Domain Driven Design Framework” to DDD “Domain Driven Design Framework” as a soft system approach of information systems development. The framework use SSM as a guiding methodology within which we have embedded a sequence of design tasks based on the UML leading to the implementation of a software system using the Naked Objects framework. This framework has been used in action research projects that have involved the investigation and modelling of business processes using object-oriented domain models and the implementation of software systems based on those domain models. Within this framework, Soft Systems Methodology (SSM) is used as a guiding methodology to explore the problem situation and to develop the domain model using UML for the given business domain. The framework is proposed and evaluated in our previous works, a comparison between SSDDD and DDD is presented in this paper, to show how SSDDD improved DDD as an approach to modelling and implementing business domain perspectives for Information Systems Development. The comparison process, the results, and the improvements are presented in the following sections of this paper.

Keywords: SSM, UML, domain-driven design, soft domain-driven design, naked objects, soft language, information retrieval, multimethodology.

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Authors: M. Rozanek, K. Roubik

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The article deals with development, design and implementation of a mathematical model of the human respiratory system. The model is designed in order to simulate distribution of important intrapulmonary parameters along the bronchial tree such as pressure amplitude, tidal volume and effect of regional mechanical lung properties upon the efficiency of various ventilatory techniques. Therefore exact agreement of the model structure with the lung anatomical structure is required. The model is based on the lung morphology and electro-acoustic analogy is used to design the model.

Keywords: Model of the respiratory system, total lung impedance, intrapulmonary parameters.

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Authors: Kamila Janovská, Šárka Vilamová, Petr Besta, Iveta Vozňáková, Roman Kozel

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Quantitative methods of economic decision-making as the methodological base of the so called operational research represent an important set of tools for managing complex economic systems,both at the microeconomic level and on the macroeconomic scale. Mathematical models of controlled and controlling processes allow, by means of artificial experiments, obtaining information foroptimalor optimum approaching managerial decision-making.The quantitative methods of economic decision-making usually include a methodology known as structural analysis -an analysisof interdisciplinary production-consumption relations.

Keywords: economic decision-making, mathematical methods, structuralanalysis, technical coefficient

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Authors: A. Al-Rifaie, Z. W. Guan, S. W. Jones

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This paper presents a method for modelling and analysing end plate beam-to-column connections to obtain the quasi-static behaviour using non-linear dynamic explicit integration. In addition to its importance to study the static behaviour of a structural member, quasi-static behaviour is largely needed to be compared with the dynamic behaviour of such members in order to investigate the dynamic effect by proposing dynamic increase factors (DIFs). The beam-to-column bolted connections contain various contact surfaces at which the implicit procedure may have difficulties converging, resulting in a large number of iterations. Contrary, explicit procedure could deal effectively with complex contacts without converging problems. Hence, finite element modelling using ABAQUS/explicit is used in this study to address the dynamic effect may be produced using explicit procedure. Also, the effect of loading rate and mass scaling are discussed to investigate their effect on the time of analysis. The results show that the explicit procedure is valuable to model the end plate beam-to-column connections in terms of failure mode, load-displacement relationships. Also, it is concluded that loading rate and mass scaling should be carefully selected to avoid the dynamic effect in the solution.

Keywords: Quasi-static, end plate, finite element, connections.

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Authors: Michaela Chovancova, Jakub Elcner

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Real bronchial tree is very complicated piping system. Analysis of flow and pressure losses in this system is very difficult. Due to the complex geometry and the very small size in the lower generations is examination by CFD possible only in the central part of bronchial tree. For specify the pressure losses of lower generations is necessary to provide a mathematical equation. Determination of mathematical formulas for calculation of pressure losses in the real lungs is time consuming and inefficient process due to its complexity and diversity. For these calculations is necessary to slightly simplify the geometry of lungs (same cross-section over the length of individual generation) or use one of the idealized models of lungs (Horsfield, Weibel). The article compares the values of pressure losses obtained from CFD simulation of air flow in the central part of the real bronchial tree with the values calculated in a slightly simplified real lungs by using a mathematical relationship derived from the Bernoulli and continuity equations. The aim of the article is to analyse the accuracy of the analytical method and its possibility of use for the calculation of pressure losses in lower generations, which is difficult to solve by numerical method due to the small geometry.

Keywords: Pressure gradient, airways resistance, real geometry of bronchial tree, breathing.

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Authors: S. A. Che Osmi, W. M. F. Wan Ishak, H. Kim, M. A. Azman, M. A. Ramli

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River is one of important water sources for many activities including industrial and domestic usage such as daily usage, transportation, power supply and recreational activities. However, increasing activities in a river has grown the sources of pollutant enters the water bodies, and degraded the water quality of the river. It becomes a challenge to develop an effective river management to ensure the water sources of the river are well managed and regulated. In Malaysia, several approaches for river management have been implemented such as Integrated River Basin Management (IRBM) program for coordinating the management of resources in a natural environment based on river basin to ensure their sustainability lead by Department of Drainage and Irrigation (DID), Malaysia. Nowadays, Total Maximum Daily Load (TMDL) is one of the best approaches for river management in Malaysia. TMDL implementation is regulated and implemented in the United States. A study on the development of TMDL in Malacca River has been carried out by doing water quality monitoring, the development of water quality model by using Environmental Fluid Dynamic Codes (EFDC), and TMDL implementation plan. The implementation of TMDL will help the stakeholders and regulators to control and improve the water quality of the river. It is one of the good approaches for river management in Malaysia.

Keywords: EFDC, river management, TMDL, water quality modelling.

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Authors: A. Breda, C. 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. 23 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: Active learning, hands-on activities, origami, creativity, critical thinking.

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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: Manisha Chaudhary, Joydip Dhar, Govind Prasad Sahu

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A mathematical model is proposed considering the forest biomass density B(t), density of wood based industries W(t) and density of synthetic industries S(t). It is assumed that the forest biomass grows logistically in the absence of wood based industries, but depletion of forestry biomass is due to presence of wood based industries. The growth of wood based industries depends on B(t), while S(t) grows at a constant rate, independent of B(t). Further there is a competition between W(t) and S(t) according to market demand. The proposed model has four ecologically feasible steady states, namely, E1: forest biomass free and wood industries free equilibrium; E2: wood industries free equilibrium and two coexisting equilibria E∗1 , E∗2 . Behavior of the system near all feasible equilibria is analyzed using the stability theory of differential equations. In the proposed model, the natural depletion rate h1 is a crucial parameter and system exhibits Hopf-bifurcation about the non-trivial equilibrium with respect to h1. The analytical results are verified using numerical simulation.

Keywords: A mathematical model, Competition between wood based and synthetic industries, Hopf-bifurcation, Stability analysis.

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Authors: Lakshmi Dhandabani, Rajeev Sukumaran

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Aim of this research study is to investigate and establish the characteristics of brain dominances (BD) and multiple intelligences (MI). This experimentation has been conducted for the sample size of 552 undergraduate computer-engineering students. In addition, mathematical formulation has been established to exhibit the relation between thinking and intelligence, and its correlation has been analyzed. Correlation analysis has been statistically measured using Pearson’s coefficient. Analysis of the results proves that there is a strong relational existence between thinking and intelligence. This research is carried to improve the didactic methods in engineering learning and also to improve e-learning strategies.

Keywords: Thinking style assessment, correlational analysis, mathematical model, data analysis, dynamic equilibrium.

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Authors: A. Ghaffari, A. S. Mostafavi

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Complex assemblies of interacting proteins carry out most of the interesting jobs in a cell, such as metabolism, DNA synthesis, mitosis and cell division. These physiological properties play out as a subtle molecular dance, choreographed by underlying regulatory networks that control the activities of cyclin-dependent kinases (CDK). The network can be modeled by a set of nonlinear differential equations and its behavior predicted by numerical simulation. In this paper, an innovative approach has been proposed that uses genetic algorithms to mine a set of behavior data output by a biological system in order to determine the kinetic parameters of the system. In our approach, the machine learning method is integrated with the framework of existent biological information in a wiring diagram so that its findings are expressed in a form of system dynamic behavior. By numerical simulations it has been illustrated that the model is consistent with experiments and successfully shown that such application of genetic algorithms will highly improve the performance of mathematical model of the cell division cycle to simulate such a complicated bio-system.

Keywords: Cell cycle, Cyclin-dependent kinase, Fission yeast, Genetic algorithms, Mathematical modeling, Wiring diagram

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Authors: Zdeňka Rendlová

Abstract:

This paper presents the mathematical description of the high-speed rotating system taking into account the influence of internal and external damping. The mathematical model is obtained by using the finite element method. The analyzed system is an automotive turbocharger understood as a rotor-bearing system. The circular cross-section shaft is equipped with one compressor wheel, one turbine wheel and is supported by two floating ring bearings. Based on the model, the dynamical analysis of a turbocharger is performed and stability conditions are evaluated.

Keywords: External damping, internal damping, journal bearing, stability, turbocharger.

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Authors: Fadi Awawdeh, O. Alsayyed

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New exact three-wave solutions including periodic two-solitary solutions and doubly periodic solitary solutions for the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov (ANNV) system are obtained using Hirota's bilinear form and generalized three-wave type of ansatz approach. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an e¤ective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.

Keywords: Soliton Solution, Hirota Bilinear Method, ANNV System.

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

Abstract:

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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