Search results for: mathematical decomposition

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: axioms, classical physics, physical concepts, relativity

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Authors: Saeideh Salimpour, Sophie-Charlotte Viaux, Ahmed Azab, Mohammed Fazle Baki

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The Facility Layout Problem (FLP) is key to the efficient and cost-effective operation of a system. This paper presents a hybrid heuristic- and mathematical-programming-based approach that divides the problem conceptually into those of clustering and sequencing. First, clusters of vertically aligned facilities are formed, which are later on sequenced horizontally. The developed methodology provides promising results in comparison to its counterparts in the literature by minimizing the inter-distances for facilities which have more interactions amongst each other and aims at placing the facilities with more interactions at the centroid of the shop.

Keywords: clustering-sequencing approach, mathematical modeling, optimization, unequal facility layout problem

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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: Gliclazide, hypromellose, drug release, modified-release tablet, mathematical model

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Authors: Divya Vats, Sanjay Mahajani

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The clarification of sugarcane juice plays a pivotal role in the production of non-centrifugal sugar (NCS), profoundly influencing the quality of the final NCS product. In this study, we have investigated the kinetics and mathematical modeling of the batch clarification process. The turbidity of the clarified cane juice (NTU) emerges as the determinant of the end product’s color. Moreover, this parameter underscores the significance of considering other variables as performance indicators for accessing the efficacy of the clarification process. Temperature-controlled experiments were meticulously conducted in a laboratory-scale batch mode. The primary objective was to discern the essential and optimized parameters crucial for augmenting the clarity of cane juice. Additionally, we explored the impact of pH and flocculant loading on the kinetics. Particle Image Velocimetry (PIV) is employed to comprehend the particle-particle and fluid-particle interaction. This technique facilitated a comprehensive understanding, paving the way for the subsequent multiphase computational fluid dynamics (CFD) simulations using the Eulerian-Lagrangian approach in the Ansys fluent. Impressively, these simulations accurately replicated comparable velocity profiles. The final mechanism of this study helps to make a mathematical model and presents a valuable framework for transitioning from the traditional batch process to a continuous process. The ultimate aim is to attain heightened productivity and unwavering consistency in product quality.

Keywords: non-centrifugal sugar, particle image velocimetry, computational fluid dynamics, mathematical modeling, turbidity

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Authors: Muleya Nqobile, Winston Garira

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We presented a compartmental deterministic multi-scale model which encompass internal plant defensive mechanism and pathogen interaction, then we consider nesting the model into the epidemiological model. The objective was to improve our understanding of the transmission dynamics of within host and between host of Guignardia citricapa Kiely. The inflow of infected class was scaled down to individual level while the outflow was scaled up to average population level. Conceptual model and mathematical model were constructed to display a theoretical framework which can be used for predicting or identify disease pattern.

Keywords: epidemiological model, mathematical modelling, multi-scale modelling, immunological model

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Authors: Min Chang Shin, Byung Hun Jeong, Jeong Sik Han, Jung Hoon Park

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In modern times, as flight speeds have increased due to improvements in aircraft and missile engine performance, thermal loads have also increased. Because of the friction heat of air flow with high speed on the surface of the vehicle, it is not easy to cool the superheat of the vehicle by the simple air cooling method. For this reason, a cooling method through endothermic heat is attracting attention by using a fuel that causes an endothermic reaction in a high-speed vehicle. There are two main ways of cooling the fuel through the endothermic reaction. The first is physical heat absorption. When the temperature rises, there is a sensible heat that accompanies it. The second is the heat of reaction corresponding to the chemical heat absorption, which absorbs heat during the fuel decomposes. Generally, since the decomposition reaction of the fuel proceeds at a high temperature, it does not achieve a great efficiency in cooling the high-speed flight body. However, when the catalyst is used, decomposition proceeds at a low temperature thereby increasing the cooling efficiency. However, when the catalyst is used as a powder, the catalyst enters the engine and damages the engine or the catalyst can deteriorate the performance due to the sintering. On the other hand, when used in the form of pellets, catalyst loss can be prevented. However, since the specific surface of pellet is small, the efficiency of the catalyst is low. And it can interfere with the flow of fuel, resulting in pressure loss and problems with fuel injection. In this study, we tried to maximize the performance of the catalyst by preparing a hollow fiber type pellet for zeolite ZSM-5, which has a higher amount of heat absorption, than other conventional pellets. The hollow fiber type pellet was prepared by phase inversion method. The hollow fiber type pellet has a finger-like pore and sponge-like pore. So it has a higher specific surface area than conventional pellets. The crystal structure of the prepared ZSM-5 catalyst was confirmed by XRD, and the characteristics of the catalyst were analyzed by TPD/TPR device. This study was conducted as part of the Basic Research Project (Pure-17-20) of Defense Acquisition Program Administration.

Keywords: catalyst, endothermic reaction, high-speed vehicle cooling, zeolite, ZSM-5

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Authors: Fahad Alsharari, Mohd Salmi Md. Noorani

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A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron-Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift AZ, x is in M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, we find a new method of calculating the topological entropy of the Motzkin shift M(M,N) without any measure theoretical discussion.

Keywords: entropy, Motzkin shift, mathematical model, theory

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Authors: Nina Philipova

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The influence of the geometric parameters of trapezoidal labyrinth channel on the pressure losses along the labyrinth length is investigated in this work. The impact of the dentate height is studied at fixed values of the dentate angle and the dentate spacing. The objective of the work presented in this paper is to derive a mathematical model of the pressure losses along the labyrinth length depending on the dentate height. The numerical simulations of the water flow movement are performed by using Commercial codes ANSYS GAMBIT and FLUENT. Dripper inlet pressure is set up to be 1 bar. As a result, the mathematical model of the pressure losses is determined as a second-order polynomial by means Commercial code STATISTIKA. Bi-objective optimization is performed by using the mean algebraic function of utility. The optimum value of the dentate height is defined at fixed values of the dentate angle and the dentate spacing. The derived model of the pressure losses and the optimum value of the dentate height are used as a basis for a more successful emitter design.

Keywords: drip irrigation, labyrinth channel hydrodynamics, numerical simulations, Reynolds stress model

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Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.

Keywords: algebra, algebraic challenge, algebraic puzzle, math rally

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Authors: Jaya Bishnu Pradhan

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Weaving mat is one of the common activities performed in different community generally in the rural part of Nepal. Mat weavers’ practice mathematical ideas and concepts implicitly in order to perform their job. This study is intended to uncover the mathematical ideas embedded in mat weaving that can help teachers and students for the teaching and learning of school geometry. The ethnographic methodology was used to uncover and describe the beliefs, values, understanding, perceptions, and attitudes of the mat weavers towards mathematical ideas and concepts in the process of mat weaving. A total of 4 mat weavers, two mathematics teachers and 12 students from grade level 6-8, who are used to participate in weaving, were selected for the study. The whole process of the mat weaving was observed in a natural setting. The classroom observation and in-depth interview were taken with the participants with the help of interview guidelines and observation checklist. The data obtained from the field were categorized according to the themes regarding mathematical ideas embedded in the weaving activities, and its possibilities in teaching learning of school geometry. In this study, the mathematical activities in different sectors of their lives, their ways of understanding the natural phenomena, and their ethnomathematical knowledge were analyzed with the notions of pluralism. From the field data, it was found that the mat weaver exhibited sophisticated geometrical ideas in the process of construction of frame of mat. They used x-test method for confirming if the mat is rectangular. Mat also provides a good opportunity to understand the space geometry. A rectangular form of mat may be rolled up when it is not in use and can be converted to a cylindrical form, which usually can be used as larder so as to reserve food grains. From the observation of the situations, this cultural experience enables students to calculate volume, curved surface area and total surface area of the cylinder. The possibilities of incorporation of these cultural activities and its pedagogical use were observed in mathematics classroom. It is argued that it is possible to use mat weaving activities in the teaching and learning of school geometry.

Keywords: ethnography, ethnomathematics, geometry, mat weaving, school pedagogy

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Authors: Morteza Khorrami

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The logic as an intellectual infrastructure plays an essential role in the Islamic sciences. Hence, there are a few of the verses of the Holy Quran that their interpretation is not possible due to lack of proper logic. In many verses in the Quran, argument and the respondent has requested from the audience that shows the logic rule is in the Quran. The paper which use a descriptive and analytic method, tries to show the role of logic in understanding of the Quran reasoning methods and display some of Quranic statements with mathematical symbols and point that we can help these symbols for interesting and interpretation and answering to some questions and doubts. In this paper, this problem has been mentioned that the Quran did not use two-valued logic (Aristotelian) in all cases, but the fuzzy logic can also be searched in the Quran.

Keywords: aristotelian logic, fuzzy logic, interpretation, Holy Quran

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Authors: Yanjie Zhu, André Jesus, Irwanda Laory

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Structural Health Monitoring (SHM), involving data acquisition, data interpretation and decision-making system aim to continuously monitor the structural performance of civil infrastructures under various in-service circumstances. The main value and purpose of SHM is identifying damages through data interpretation system. Research on SHM has been expanded in the last decades and a large volume of data is recorded every day owing to the dramatic development in sensor techniques and certain progress in signal processing techniques. However, efficient and reliable data interpretation for damage detection under environmental variations is still a big challenge. Structural damages might be masked because variations in measured data can be the result of environmental variations. This research reports a novel method based on single-channel Blind Signal Separation (BSS), which extracts environmental effects from measured data directly without any prior knowledge of the structure loading and environmental conditions. Despite the successful application in audio processing and bio-medical research fields, BSS has never been used to detect damage under varying environmental conditions. This proposed method optimizes and combines Ensemble Empirical Mode Decomposition (EEMD), Principal Component Analysis (PCA) and Independent Component Analysis (ICA) together to separate structural responses due to different loading conditions respectively from a single channel input signal. The ICA is applying on dimension-reduced output of EEMD. Numerical simulation of a truss bridge, inspired from New Joban Line Arakawa Railway Bridge, is used to validate this method. All results demonstrate that the single-channel BSS-based method can recover temperature effects from mixed structural response recorded by a single sensor with a convincing accuracy. This will be the foundation of further research on direct damage detection under varying environment.

Keywords: damage detection, ensemble empirical mode decomposition (EEMD), environmental variations, independent component analysis (ICA), principal component analysis (PCA), structural health monitoring (SHM)

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Authors: Mohammed Darwish

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Workplace injuries cost organizations significant amount of money. Causes of injuries at workplace are very well documented in the literature and attributed to variety of reasons. One important reason is the long working-hours. The purpose of this paper is to develop a mathematical model that finds the optimal working-hours at workplace. The developed model minimizes the expected total cost which consists of the expected cost incurred due to unsafe conditions of workplace, the other cost is related to the lost production due to work incidents, and the production cost.

Keywords: 8-hour workday, mathematical model, optimal working hours, workplace injuries

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Authors: Ganiyat Soliu, Glen Bright, Chiemela Onunka

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Performance optimization plays a key role in controlling the waiting time during manufacturing in an advanced manufacturing environment to improve productivity. Queuing mathematical modeling theory was used to examine the performance of the multi-stage production line. Robotics as a disruptive technology was implemented into a virtual manufacturing scenario during the packaging process to study the effect of waiting time on productivity. The queuing mathematical model was used to determine the optimum service rate required by robots during the packaging stage of manufacturing to yield an optimum production cost. Different rates of production were assumed in a virtual manufacturing environment, cost of packaging was estimated with optimum production cost. An equation was generated using queuing mathematical modeling theory and the theorem adopted for analysis of the scenario is the Newton Raphson theorem. Queuing theory presented here provides an adequate analysis of the number of robots required to regulate waiting time in order to increase the number of output. Arrival rate of the product was fast which shows that queuing mathematical model was effective in minimizing service cost and the waiting time during manufacturing. At a reduced waiting time, there was an improvement in the number of products obtained per hour. The overall productivity was improved based on the assumptions used in the queuing modeling theory implemented in the virtual manufacturing scenario.

Keywords: performance optimization, productivity, queuing theory, robotics

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Authors: Uliana N. Tumanova, Viacheslav M. Lyapin, Vladimir G. Bychenko, Alexandr I. Shchegolev, Gennady T. Sukhikh

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It is well known that the gas formed as a result of postmortem decomposition of tissues can be detected already 24-48 hours after death. In addition, the conditions of keeping and storage of the corpse (temperature and humidity of the environment) significantly determine the rate of occurrence and development of posthumous changes. The presence of sepsis is accompanied by faster postmortem decomposition and decay of the organs and tissues of the body. The presence of gas in the vessels and cavities can be revealed fully at postmortem CT. Radiologists must certainly report on the detection of intraorganic or intravascular gas, wich was detected at postmortem CT, to forensic experts or pathologists before the autopsy. This gas can not be detected during autopsy, but it can be very important for establishing a diagnosis. To explore the possibility of postmortem CT for the evaluation of gas accumulations in the newborns' vessels, who died from congenital sepsis. Researched of 44 newborns bodies (25 male and 19 female sex, at the age from 6 hours to 27 days) after 6 - 12 hours of death. The bodies were stored in the refrigerator at a temperature of +4°C in the supine position. Grouped 12 bodies of newborns that died from congenital sepsis. The control group consisted of 32 bodies of newborns that died without signs of sepsis. Postmortem CT examination was performed at the GEMINI TF TOF16 device, before the autopsy. The localizations of gas accumulations in the vessels were determined on the CT tomograms. The sepsis diagnosis was on the basis of clinical and laboratory data and autopsy results. Gases in the vessels were detected in 33.3% of cases in the group with sepsis, and in the control group - in 34.4%. A group with sepsis most often the gas localized in the heart and liver vessels - 50% each, of observations number with the detected gas in the vessels. In the heart cavities, aorta and mesenteric vessels - 25% each. In control most often gas was detected in the liver (63.6%) and abdominal cavity (54.5%) vessels. In 45.5% the gas localized in the cavities, and in 36.4% in the vessels of the heart. In the cerebral vessels and in the aorta gas was detected in 27.3% and 9.1%, respectively. Postmortem CT has high diagnostic capabilities to detect free gas in vessels. Postmortem changes in newborns that died from sepsis do not affect intravascular gas production within 6-12 hours. Radiation methods should be used as a supplement to the autopsy, including as a kind of ‘guide’, with the indication to the forensic medical expert of certain changes identified during CT studies, for better definition of pathological processes during the autopsy. Postmortem CT can be recommend as a first stage of autopsy.

Keywords: congenital sepsis, gas, newborn, postmortem CT

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Authors: Khashayar Kazemzadeh, Mohammad Hanif Dasoomi

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According to the increasing travel demand in cities, bridges and tunnels are viewed as one of the fundamental components of cities transportation systems. Normally, due to geometric constraints forms in the tunnels, the considered speed in the tunnels is lower than the speed in connected highways. Therefore, drivers tend to reduce the speed near the entrance of the tunnels. In this paper, the effect of speed reduction on accident happened in the entrance of the tunnels has been discussed. The relation between accidents frequency and the parameters of speed, traffic volume and time of the accident in the mentioned tunnel has been analyzed and the mathematical model has been proposed.

Keywords: urban highway, accident, tunnel, mathematical model

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Authors: Ogunrinde Roseline Bosede, Ogunrinde Rowland Rotimi

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Just as the development of ideas of early mathematics was essentially motivated by social needs, the invention of the computer was equally inspired by social needs. The early years of the twenty-first century have been remarkable in advances in mathematical and computer sciences. Mathematical and computer sciences work are fast becoming an increasingly integral and essential components of a growing catalogues of areas of interests in biology, business, military, medicine, social sciences, advanced design, advanced materials, climate, banking and finance, and many other fields of disciplines. This paper seeks to highlight the trend and impacts of the duo in the technological advancements being witnessed in our today's world.

Keywords: computer, impacts, mathematics, modern society

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Authors: Mohamed Amarouayache, Badia Amrouche, Gharbi Akila, Boukadoume Mohamed

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This work is devoted to the modeling of DC-DC converter (boost) used for MPPT applications to set conditions of stability. For this, we establish a linear mathematical model of the DC-DC converter with an average small signal model. This model has allowed us to apply conventional linear methods of automation. A mathematical relationship between the duty cycle and the voltage of the panel has been set up. With this relationship we specify the conditions of the stability in closed-loop depending on the system parameters (the elements of storage capacity and inductance, PWM control).

Keywords: MPPT, PWM, stability, criterion of Routh, average small signal model

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Authors: Chakib Jerry, Mounir Jerry

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In this paper, a mathematical model of infested honey bees colonies is formulated in order to investigate Colony Collapse Disorder in a honeybee colony. CCD, as it is known, is a major problem on honeybee farms because of the massive decline in colony numbers. We introduce to the model a control variable which represents forager protection. We study the controlled model to derive conditions under which the bee colony can fight off epidemic. Secondly we study the problem of minimizing prevention cost under model’s dynamics constraints.

Keywords: honey bee, disease transmission model, disease control honeybees, optimal control

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Authors: Sofia N. Gonçalves, Duarte M. S. Albuquerque, José C. F. Pereira

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The energy transition is spurred by structural changes in energy demand, supply, and prices. Microwave technology was first proposed as a faster alternative for cooking food. It was found that food heated instantly when interacting with high-frequency electromagnetic waves. The dielectric properties account for a material’s ability to absorb electromagnetic energy and dissipate this energy in the form of heat. Many energy-intense industries could benefit from electromagnetic heating since many of the raw materials are dielectric at high temperatures. Limestone sedimentary rock is a dielectric material intensively used in the cement industry to produce unslaked lime. A numerical 3D model was implemented in COMSOL Multiphysics to study the limestone continuous processing under microwave heating. The model solves the two-way coupling between the Energy equation and Maxwell’s equations as well as the coupling between heat transfer and chemical interfaces. Complementary, a controller was implemented to optimize the overall heating efficiency and control the numerical model stability. This was done by continuously matching the cavity impedance and predicting the required energy for the system, avoiding energy inefficiencies. This controller was developed in MATLAB and successfully fulfilled all these goals. The limestone load influence on thermal decomposition and overall process efficiency was the main object of this study. The procedure considered the Verification and Validation of the chemical kinetics model separately from the coupled model. The chemical model was found to correctly describe the chosen kinetic equation, and the coupled model successfully solved the equations describing the numerical model. The interaction between flow of material and electric field Poynting vector revealed to influence limestone decomposition, as a result from the low dielectric properties of limestone. The numerical model considered this effect and took advantage from this interaction. The model was demonstrated to be highly unstable when solving non-linear temperature distributions. Limestone has a dielectric loss response that increases with temperature and has low thermal conductivity. For this reason, limestone is prone to produce thermal runaway under electromagnetic heating, as well as numerical model instabilities. Five different scenarios were tested by considering a material fill ratio of 30%, 50%, 65%, 80%, and 100%. Simulating the tube rotation for mixing enhancement was proven to be beneficial and crucial for all loads considered. When uniform temperature distribution is accomplished, the electromagnetic field and material interaction is facilitated. The results pointed out the inefficient development of the electric field within the bed for 30% fill ratio. The thermal efficiency showed the propensity to stabilize around 90%for loads higher than 50%. The process accomplished a maximum microwave efficiency of 75% for the 80% fill ratio, sustaining that the tube has an optimal fill of material. Electric field peak detachment was observed for the case with 100% fill ratio, justifying the lower efficiencies compared to 80%. Microwave technology has been demonstrated to be an important ally for the decarbonization of the cement industry.

Keywords: CFD numerical simulations, efficiency optimization, electromagnetic heating, impedance matching, limestone continuous processing

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Authors: Azam Zare

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Separation flow control for performance enhancement over airfoils at high incidence angle has become an increasingly important topic. This work details the characteristics of an efficient feedback control of the turbulent subsonic flow over NACA23012 airfoil using forced reduced‐order model based on the proper orthogonal decomposition/Galerkin projection and perturbation method on the compressible Reynolds Averaged Navier‐Stokes equations. The forced reduced‐order model is used in the optimal control of the turbulent separated flow over a NACA23012 airfoil at Mach number of 0.2, Reynolds number of 5×106, and high incidence angle of 24° using blowing/suction controlling jets. The Spallart-Almaras turbulence model is implemented for high Reynolds number calculations. The main shortcoming of the POD/Galerkin projection on flow equations for controlling purposes is that the blowing/suction controlling jet velocity does not show up explicitly in the resulting reduced order model. Combining perturbation method and POD/Galerkin projection on flow equations introduce a forced reduced‐order model that can predict the time-varying influence of the blowing/suction controlling jet velocity. An optimal control theory based on forced reduced‐order system is used to design a control law for a nonlinear reduced‐order model, which attempts to minimize the vorticity content in the turbulent flow field over NACA23012 airfoil. Numerical simulations were performed to help understand the behavior of the controlled suction jet at 12% to 18% chord from leading edge and a pair of blowing/suction jets at 15% to 18% and 24% to 30% chord from leading edge, respectively. Analysis of streamline profiles indicates that the blowing/suction jets are efficient in removing separation bubbles and increasing the lift coefficient up to 22%, while the perturbation method can predict the flow field in an accurate Manner.

Keywords: flow control, POD, Galerkin projection, separation

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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: Ling Zhang, Weikai Li

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Recently three sufficient conditions for the three-way Candecomp/Parafac (CP) model which ensure uniqueness in one of the three modes(“uni-mode uniqueness”) are given. In this paper, we generalize these uniqueness conditions to n ≤ 3 and give a sufficient conditions for the n-way Candecomp/Parafac (CP) model, which ensure uniqueness in one of the n modes.

Keywords: uni-mode uniqueness, candecomp/parafac, n-way arrays, decomposition, tensor

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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: Laura Salvia Diaz Silvarrey, Anh Phan

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Municipal Plastic Waste (MPW) comprises a mixture of thermoplastics such as high and low density polyethylene (HDPE and LDPE), polypropylene (PP), polystyrene (PS) and polyethylene terephthalate (PET). Recycling rate of these plastics is low, e.g. only 27% in 2013. The remains were incinerated or disposed in landfills. As MPW generation increases approximately 5% per annum, MPW management technologies have to be developed to comply with legislation . Pyrolysis, thermochemical decomposition, provides an excellent alternative to convert MPW into valuable resources like fuels and chemicals. Most studies on waste plastic kinetics only focused on HDPE and LDPE with a simple assumption of first order decomposition, which is not the real reaction mechanism. The aim of this study was to develop a kinetic study for each of the polymers in the MPW mixture using thermogravimetric analysis (TGA) over a range of heating rates (5, 10, 20 and 40°C/min) in N2 atmosphere and sample size of 1 – 4mm. A model-free kinetic method was applied to quantify the activation energy at each level of conversion. Kissinger–Akahira–Sunose (KAS) and Flynn–Wall–Ozawa (FWO) equations jointly with Master Plots confirmed that the activation energy was not constant along all the reaction for all the five plastic studied, showing that MPW decomposed through a complex mechanism and not by first-order kinetics. Master plots confirmed that MPW decomposed following a random scission mechanism at conversions above 40%. According to the random scission mechanism, different radicals are formed along the backbone producing the cleavage of bonds by chain scission into molecules of different lengths. The cleavage of bonds during random scission follows first-order kinetics and it is related with the conversion. When a bond is broken one part of the initial molecule becomes an unsaturated one and the other a terminal free radical. The latter can react with hydrogen from and adjacent carbon releasing another free radical and a saturated molecule or reacting with another free radical and forming an alkane. Not every time a bonds is broken a molecule is evaporated. At early stages of the reaction (conversion and temperature below 40% and 300°C), most products are not short enough to evaporate. Only at higher degrees of conversion most of cleavage of bonds releases molecules small enough to evaporate.

Keywords: kinetic, municipal plastic waste, pyrolysis, random scission

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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: Zahid Ullah, Atlas Khan

Abstract:

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: Tri Wijayanti Septiarini, Agus Maman Abadi, Muhammad Rifki Taufik

Abstract:

The exchange rate of IDR/USD can be the indicator to analysis Indonesian economy. The exchange rate as a important factor because it has big effect in Indonesian economy overall. So, it needs the analysis data of exchange rate. There is decomposition data of exchange rate of IDR/USD to be frequency and time. It can help the government to monitor the Indonesian economy. This method is very effective to identify the case, have high accurate result and have simple structure. In this paper, data of exchange rate that used is weekly data from December 17, 2010 until November 11, 2014.

Keywords: the exchange rate, fuzzy mamdani, discrete wavelet transforms, fuzzy wavelet

Procedia PDF Downloads 540

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

Abstract:

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.

Procedia PDF Downloads 145