Search results for: mathematical music modelling

Authors: Ella Tyuryumina, Alexey Neznanov

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This study is an attempt to obtain reliable data on the natural history of breast cancer growth. We analyze the opportunities for using classical mathematical models (exponential and logistic tumor growth models, Gompertz and von Bertalanffy tumor growth models) to try to describe growth of the primary tumor and the secondary distant metastases of human breast cancer. The research aim is to improve predicting accuracy of breast cancer progression using an original mathematical model referred to CoMPaS and corresponding software. We are interested in: 1) modelling the whole natural history of the primary tumor and the secondary distant metastases; 2) developing adequate and precise CoMPaS which reflects relations between the primary tumor and the secondary distant metastases; 3) analyzing the CoMPaS scope of application; 4) implementing the model as a software tool. The foundation of the CoMPaS is the exponential tumor growth model, which is described by determinate nonlinear and linear equations. The CoMPaS corresponds to TNM classification. It allows to calculate different growth periods of the primary tumor and the secondary distant metastases: 1) ‘non-visible period’ for the primary tumor; 2) ‘non-visible period’ for the secondary distant metastases; 3) ‘visible period’ for the secondary distant metastases. The CoMPaS is validated on clinical data of 10-years and 15-years survival depending on the tumor stage and diameter of the primary tumor. The new predictive tool: 1) is a solid foundation to develop future studies of breast cancer growth models; 2) does not require any expensive diagnostic tests; 3) is the first predictor which makes forecast using only current patient data, the others are based on the additional statistical data. The CoMPaS model and predictive software: a) fit to clinical trials data; b) detect different growth periods of the primary tumor and the secondary distant metastases; c) make forecast of the period of the secondary distant metastases appearance; d) have higher average prediction accuracy than the other tools; e) can improve forecasts on survival of breast cancer and facilitate optimization of diagnostic tests. The following are calculated by CoMPaS: the number of doublings for ‘non-visible’ and ‘visible’ growth period of the secondary distant metastases; tumor volume doubling time (days) for ‘non-visible’ and ‘visible’ growth period of the secondary distant metastases. The CoMPaS enables, for the first time, to predict ‘whole natural history’ of the primary tumor and the secondary distant metastases growth on each stage (pT1, pT2, pT3, pT4) relying only on the primary tumor sizes. Summarizing: a) CoMPaS describes correctly the primary tumor growth of IA, IIA, IIB, IIIB (T1-4N0M0) stages without metastases in lymph nodes (N0); b) facilitates the understanding of the appearance period and inception of the secondary distant metastases.

Keywords: breast cancer, exponential growth model, mathematical model, metastases in lymph nodes, primary tumor, survival

Procedia PDF Downloads 341

Authors: Ebuwa Osagie, Chet Biliyok, Yeung Hoi

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Regeneration energy requirement and ways to reduce it is the main aim of most CO2 capture researches currently being performed and thus, post-combustion carbon capture (PCC) option is identified to be the most suitable for the natural gas-fired power plants. From current research and development (R&D) activities worldwide, two main areas are being examined in order to reduce the regeneration energy requirement of amine-based PCC, namely: (a) development of new solvents with better overall performance than 30wt% monoethanolamine (MEA) aqueous solution, which is considered as the base-line solvent for solvent-based PCC, (b) Integration of the PCC Plant to the power plant. In scaling-up a PCC pilot plant to the size required for a commercial-scale natural gas-fired power plant, process modelling and simulation is very essential. In this work, an integrated process made up of a 482MWe natural gas-fired power plant, an MEA-based PCC plant which is developed and validated has been modelled and simulated. The PCC plant has four absorber columns and a single stripper column, the modelling and simulation was performed with Aspen Plus® V8.4. The gas turbine, the heat recovery steam generator and the steam cycle were modelled based on a 2010 US DOE report, while the MEA-based PCC plant was modelled as a rate-based process. The scaling of the amine plant was performed using a rate based calculation in preference to the equilibrium based approach for 90% CO2 capture. The power plant was integrated to the PCC plant in three ways: (i) flue gas stream from the power plant which is divided equally into four stream and each stream is fed into one of the four absorbers in the PCC plant. (ii) Steam draw-off from the IP/LP cross-over pipe in the steam cycle of the power plant used to regenerate solvent in the reboiler. (iii) Condensate returns from the reboiler to the power plant. The integration of a PCC plant to the NGCC plant resulted in a reduction of the power plant output by 73.56 MWe and the net efficiency of the integrated system is reduced by 7.3 % point efficiency. A secondary aim of this study is the parametric studies which have been performed to assess the impacts of natural gas on the overall performance of the integrated process and this is achieved through investigation of the capture efficiencies.

Keywords: natural gas-fired, power plant, MEA, CO2 capture, modelling, simulation

Procedia PDF Downloads 446

Authors: M. C. A. Leite, B. Chen-Charpentier, F. Agusto

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A long-term goal of sustainable forest management is a relatively stable source of wood and a stable forest age-class structure has become the goal of many forest management practices. In the absence of disturbances, this forest management goal could easily be achieved. However, in the face of recurring insect outbreaks and other disruptive processes forest planning becomes more difficult, requiring knowledge of the effects on the forest of a wide variety of environmental factors (e.g., habitat heterogeneity, fire size and frequency, harvesting, insect outbreaks, and age distributions). The association between distinct forest disturbances and the potential effect on forest dynamics is a complex matter, particularly when evaluated over time and at large scale, and is not well understood. However, gaining knowledge in this area is crucial for a sustainable forest management. Mathematical modeling is a tool that can be used to broader the understanding in this area. In this talk we will introduce mathematical models formulation incorporating the effect of insect outbreaks either as a single disturbance in the forest population dynamics or coupled with other disturbances: either wildfire or harvesting. The results and ecological insights will be discussed.

Keywords: age-structured forest population, disturbances interaction, harvesting insects outbreak dynamics, mathematical modeling

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Authors: R. Devicharan

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In a short span 3D Printing is expected to play a vital role in our life. The possibility of creativity and speed in manufacturing through various 3D printing processes is infinite. This study is performed on the FDM (Fused Deposition Modelling) method of 3D printing, which is one of the pre-dominant methods of 3D printing technologies. This study focuses on physical properties of the objects produced by 3D printing which determine the applications of the 3D printed objects. This paper specifically aims at the study of the tensile strength and the folding endurance of the 3D printed objects through the FDM (Fused Deposition Modelling) method using the ABS (Acronitirile Butadiene Styrene) and PLA (Poly Lactic Acid) plastic materials. The study is performed on a controlled environment and the specific machine settings. Appropriate tables, graphs are plotted and research analysis techniques will be utilized to analyse, verify and validate the experiment results.

Keywords: FDM process, 3D printing, ABS for 3D printing, PLA for 3D printing, rapid prototyping

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Authors: Manjula Sutagundar, B. G. Sheeparamatti, D. S. Jangamshetti

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Micro Electro Mechanical Systems (MEMS) resonators have shown the potential of replacing quartz crystal technology for sensing and high frequency signal processing applications because of inherent advantages like small size, high quality factor, low cost, compatibility with integrated circuit chips. This paper presents the optimization and modelling and simulation of the optimized micro cantilever resonator. The objective of the work is to optimize the dimensions of a micro cantilever resonator for a specified range of resonant frequency and specific quality factor. Optimization is carried out using genetic algorithm. The genetic algorithm is implemented using MATLAB. The micro cantilever resonator is modelled in CoventorWare using the optimized dimensions obtained from genetic algorithm. The modeled cantilever is analysed for resonance frequency.

Keywords: MEMS resonator, genetic algorithm, modelling and simulation, optimization

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Authors: Amirhossein Karamoozian, Desheng Wu, Behzad Abbasnejad

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Building information modelling (BIM) is a new technology to enhance the efficiency of project management in the construction industry. In addition to the potential benefits of this useful technology, there are various risks and obstacles to applying it in construction projects. In this study, a decision making approach is presented for risk assessment in BIM adoption in construction projects. Various risk factors of exerting BIM during different phases of the project lifecycle are identified with the help of Delphi method, experts’ opinions and related literature. Afterward, Shannon’s entropy and Fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Situation) are applied to derive priorities of the identified risk factors. Results indicated that lack of knowledge between professional engineers about workflows in BIM and conflict of opinions between different stakeholders are the risk factors with the highest priority.

Keywords: risk, BIM, fuzzy TOPSIS, construction projects

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Authors: Nana Saralidze, Nino Sharashenidze, Zurab Kevanishvili

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Hidden hearing loss may occur in humans exposed to prolonged high-level sound. It is the loss of ability to hear high-level background noise while having normal hearing in quiet. We compared the hearing of people who regularly listen 3 hours and more to personal music players and those who do not. Forty participants aged 18-30 years were divided into two groups: regular users of music players and people who had never used them. And the third group – elders aged 50-55 years, had 15 participants. Pure-tone audiometry (125-16000 Hz), auditory brainstem response (ABR) (70dB SPL), and ability to identify speech in noise (4-talker babble with a 65-dB signal-to-noise ratio at 80 dB) were measured in all participants. All participants had normal pure-tone audiometry (all thresholds < 25 dB HL). A significant difference between groups was observed in that regular users of personal audio systems correctly identified 53% of words, whereas the non-users identified 74% and the elder group – 63%. This contributes evidence supporting the presence of a hidden hearing loss in humans and demonstrates that speech-in-noise audiometry is an effective method and can be considered as the GOLD standard for detecting hidden hearing loss.

Keywords: mp3 player, hidden hearing loss, speech audiometry, pure tone audiometry

Procedia PDF Downloads 74

Authors: Agata Tomaszewska, Timothy Kamps, Stephan R. Turnock, Nicola Symonds

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Bob skeleton is a highly competitive sport in which an athlete reaches speeds up to 40 m/s sliding, head first, down an ice track. It is believed that the friction between the runners and ice significantly contributes to the amount of the total energy loss during a bob skeleton descent. There is only limited available experimental data regarding the friction of bob skeleton runners or indeed steel on the ice at high sliding speeds ( > 20 m/s). Testing methods used to investigate the friction of steel on ice in winter sports have been outlined, and their accuracy and repeatability discussed. A system thinking approach was used to investigate the runner-ice interaction during sliding and create concept designs of three ice tribometers. The operational envelope of the bob skeleton system has been defined through mathematical modelling. Designs of a drum, linear and inertia pin-on-disk tribometers were developed specifically for bob skeleton runner testing with the requirement of reaching up to 40 m/s speed and facilitate fresh ice sliding. The design constraints have been outline and the proposed solutions compared based on the ease of operation, accuracy and the development cost.

Keywords: bob skeleton, ice friction, high-speed tribometers, sliding friction

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Authors: Anthony Cogrove, Shagun Saikia, Pradeep Deshpande

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Introduction: Management of anxiety in rehabilitation setting often is a challenge and is usually done by using medication. The role of psychology and the creation of a quite environment in order to reduce stimulation helps in the process. We have a hypothesis that feedback from a calm visual imagery with soothing music help in reducing anxiety in these setting Aim-To explore the possibility of using virtual reality in the management of anxiety in a setting of neuro-rehabilitation unit. Method: Six patients in an inpatient rehabilitation unit with acquired brain injury subjected to a low stimulation calming visual motion picture with calm music. Six sessions were conducted over 6 weeks. All sessions were performed in a separate purpose built room in the unit. . A cohort of 6 people with various neurological conditions were involved in 6 sessions of 30 minutes during their inpatient rehabilitation. They reported benefit from using the virtual reality environment in reducing their anxiety. Results: All reported improvement in their anxiety levels. They felt there was a calming effect of the session. There was a sense of feeling of self empowerment on direct questioning. Conclusion: Virtual reality environment can aid the traditional rehabilitation techniques used to manage the levels of anxiety experienced by people with acquired brain injury undergoing inpatient rehabilitation.

Keywords: neurological rehabilitation, virtual reality, anxiety, calming environment

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Authors: W. Linthicum-Blackhorse, P. Martens

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This present study seeks to discover attitudinal commonalities and differences within a musician population relative to the communication of emotion via music. We hypothesized that instrument type, as well as age and gender, would bear significantly on musicians’ opinions. A survey was administered to 178 participants; 152 were current music majors (mean age 20.3 years, 62 female) and 26 were adult participants in a community choir (mean age 54.0 years, 12 female). The adult participants were all vocalists, while student participants represented the full range of orchestral instruments. The students were grouped by degree program, (performance, music education, or other) and instrument type (voice, brass, woodwinds, strings, percussion). The survey asked 'How important are each of the following areas to you for portraying emotion in music?' Participants were asked to rate each of 15 items on a scale of 1 (not at all important) to 10 (very important). Participants were also instructed to leave blank any item that they did not understand. The 15 items were: dynamic contrast, overall volume, phrasing, facial expression, staging (placement), pitch accuracy, tempo changes, bodily movement, your mood, your attitude, vibrato, rubato, stage/room lighting, clothing type, and clothing color. Contrary to our hypothesis, there was no overall effect of gender or age, and neither did any single response item show a significant difference due to these subject parameters. Among the student participants, however, one-way ANOVA revealed a significant effect of degree program on the rated importance of four items: dynamic contrast, tempo changes, vibrato, and rubato. Significant effects of instrument type were found in the responses to eight items: facial expression, staging, body movement, vibrato, rubato, lighting, clothing type, and clothing color. Post hoc comparisons (Tukey) show that some variation follows from obvious differences between instrument types (e.g. string players are more concerned with vibrato than everyone but woodwind players; vocalists are significantly more concerned with facial expression than everyone but string players), but other differences could point to communal mindsets toward vicarious cues within instrument type. These mindsets could be global (e.g. brass players deeming body movement significantly less important than string players, being less often featured as soloists and appearing less often at the front of the stage) or local (e.g. string players being significantly more concerned than all other groups about both clothing color and type, perhaps due to the strongly-expressed opinions of specific teachers). Future work will attempt to identify the source of these self-appraisals, whether enculturated via explicit pedagogy, or whether absorbed from individuals' observations and performance experience.

Keywords: performance, vicarious cues, communication, emotion

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Authors: Harche Rima, Laoufi Nadia Aicha

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This work focuses on the study and modeling of the fouling phenomenon in a vertical pipe. In the first step, milk is one of the fluids obeying the phenomenon of fouling because of the denaturation of these proteins, especially lactoglobulin, which is the active element of milk, and to facilitate its use, we chose to study milk as a fouling fluid. In another step, we consider the test section of our installation as a tubular-type heat exchanger that works against the current and in a closed circuit. A simple mathematical model of Kern & Seaton, based on the kinetics of the fouling resistance, was used to evaluate the influence of the operating parameters (fluid flow velocity and exchange wall temperature) on the fouling resistance. The influence of the variation of the fouling resistance with the operating conditions on the efficiency of the heat exchanger and the importance of the dirty state exchange coefficient as an exchange quality control parameter were discussed and examined. On the other hand, an electronic scanning microscope analysis was performed on the milk deposit in order to obtain its actual image and composition, which allowed us to calculate the thickness of this deposit.

Keywords: fouling, milk, tubular heat exchanger, fouling resistance

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Authors: Carlos Caro, Ernest Bladé, Pedro Acosta, Camilo Lesmes

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The drying-wet process is one of the topics to be more careful in distributed hydrological modeling using finite volume schemes as a means of solving the equations of Saint Venant. In a hydrologic and hydraulic computer model, surface flow phenomena depend mainly on the different flow accumulation and subsequent runoff generation. These accumulations are generated by routing, cell by cell, from the heights of water, which begin to appear due to the rain at each instant of time. Determine when it is considered a dry cell and when considered wet to include in the full calculation is an issue that directly affects the quantification of direct runoff or generation of flow at the end of a zone of contribution by accumulations flow generated from cells or finite volume.

Keywords: hydrology, transport processes, hydrological modelling, finite volume schemes

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Authors: Yuan-Jye Tseng, Shin-Han Lin

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In this research, a mathematical model for integrated evaluation of green design and green manufacturing processes is presented. To design a product, there can be alternative options to design the detailed components to fulfill the same product requirement. In the design alternative cases, the components of the product can be designed with different materials and detailed specifications. If several design alternative cases are proposed, the different materials and specifications can affect the manufacturing processes. In this paper, a new concept for integrating green design and green manufacturing processes is presented. A green design can be determined based the manufacturing processes of the designed product by evaluating the green criteria including energy usage and environmental impact, in addition to the traditional criteria of manufacturing cost. With this concept, a mathematical model is developed to find the green design and the associated green manufacturing processes. In the mathematical model, the cost items include material cost, manufacturing cost, and green related cost. The green related cost items include energy cost and environmental cost. The objective is to find the decisions of green design and green manufacturing processes to achieve the minimized total cost. In practical applications, the decision-making can be made to select a good green design case and its green manufacturing processes. In this presentation, an example product is illustrated. It shows that the model is practical and useful for integrated evaluation of green design and green manufacturing processes.

Keywords: supply chain management, green supply chain, green design, green manufacturing, mathematical model

Procedia PDF Downloads 807

Authors: M. Rodionov, Z. Dedovets

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The level and type of student academic motivation are the key factors in their development and determine the effectiveness of their education. Improving motivation is very important with regard to courses on middle school mathematics. This article examines the general position regarding the practice of academic motivation. It also examines the particular features of mathematical problem solving in a school setting.

Keywords: teaching strategy, mathematics, motivation, student

Procedia PDF Downloads 445

Authors: Nilson Barbieri, Bruno Matos Martins, Gabriel de Sant'Anna Vitor Barbieri

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In more complex systems, such as automotive gearbox, a rigorous treatment of the data is necessary because there are several moving parts (gears, bearings, shafts, etc.), and in this way, there are several possible sources of errors and also noise. The basic objective of this work is the detection of damage in automotive gearbox. The detection methods used are the wavelet method, the bispectrum; advanced filtering techniques (selective filtering) of vibrational signals and mathematical morphology. Gearbox vibration tests were performed (gearboxes in good condition and with defects) of a production line of a large vehicle assembler. The vibration signals are obtained using five accelerometers in different positions of the sample. The results obtained using the kurtosis, bispectrum, wavelet and mathematical morphology showed that it is possible to identify the existence of defects in automotive gearboxes.

Keywords: automotive gearbox, mathematical morphology, wavelet, bispectrum

Procedia PDF Downloads 473

Authors: Mechlouch Ridha Fethi

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This paper presents a recent mathematical model in political sciences concerning democracy. The model is represented by a logarithmic equation linking the Relative Index of Democracy (RID) to Participation Ratio (PR). Firstly the meanings of the different parameters of the model were presented; and the variation curve of the RID according to PR with different critical areas was discussed. Secondly, the model was applied to a virtual group where we show that the model can be applied depending on the gender. Thirdly, it was observed that the model can be extended to different language models of democracy and that little use to assess the state of democracy for some International organizations like UNO.

Keywords: democracy, mathematic, modelization, quantification

Procedia PDF Downloads 368

Authors: Pham Van Nha, Le Cam Binh

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Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: analysis of optimization, artificial intelligence based optimization, optimization for learning and data analysis, global optimization

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Authors: Nurudeen Oluwasola Lasisi

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The COVID-19 is an infection caused by coronavirus, which has been designated as a pandemic in the world. In this paper, we proposed a model to study the effect of distancing and wearing masks on the transmission of COVID-19 infection dynamics. The invariant region of the model is established. The COVID-19 free equilibrium and the reproduction number of the model were obtained. The local and global stability of the model is determined using the linearization technique method and Lyapunov method. It was found that COVID-19 free equilibrium state is locally asymptotically stable in feasible region Ω if R₀ < 1 and globally asymptomatically stable if R₀ < 1, otherwise unstable if R₀ > 1. More so, numerical analysis and simulations of the dynamics of the COVID-19 infection are presented.

Keywords: distancing, reproduction number, wearing of mask, local and global stability, modelling, transmission

Procedia PDF Downloads 138

Authors: Rokhmatul Insani, Hira Laksmiwati Soemitro

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Business Intelligence is a methodology that exploits the data to produce information and knowledge systematically, business intelligence can support the decision-making process. Some methods in business intelligence are data warehouse and data mining. A data warehouse can store historical data from transactional data. For data modelling in data warehouse, we apply dimensional modelling by Kimball. While data mining is used to extracting patterns from the data and get insight from the data. Data mining has many techniques, one of which is segmentation. For profiling of telecommunication customer, we use customer segmentation according to customer’s usage of services, customer invoice and customer payment. Customers can be grouped according to their characteristics and can be identified the profitable customers. We apply K-Means Clustering Algorithm for segmentation. The input variable for that algorithm we use RFM (Recency, Frequency and Monetary) model. All process in data mining, we use tools IBM SPSS modeller.

Keywords: business intelligence, customer segmentation, data warehouse, data mining

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Authors: Faisal A. Aburub

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Organizations today need to invest in software in order to run their businesses, and to the organizations’ objectives, the software should be in line with the business process. This research presents an approach for linking process models and system models. Particularly, the new approach aims to synthesize sequence diagram based on role activity diagram (RAD) model. The approach includes four steps namely: Create business process model using RAD, identify computerized activities, identify entities in sequence diagram and identify messages in sequence diagram. The new approach has been validated using the process of student registration in University of Petra as a case study. Further research is required to validate the new approach using different domains.

Keywords: business process modelling, system models, role activity diagrams, sequence diagrams

Procedia PDF Downloads 384

Authors: Redhouane Benfares, Kamel Boudjemaa, Affaf Kord, Sonia Messis, Linda Farai, Belkacem Guenachi, Kherarba Maha, Jaroslava ŠVarc-Gajić

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In recent years valorization of biowaste has attracted a lot of attention worldwide owing to its high nutritional value and low price. In this work, biowaste of animal (sardines) and plant (tomato) biowaste was used to formulate a new feed for red tilapia that showed to be competitive in its price, and zootechnical performance in comparison to commercially available tilapia feeds. Mathematical modelling was used to formulate optimal feed composition with favorable chemical composition and the lowest price. Formulated feed had high protein content (40.76%) and an energy value of 279.6 Kcal/100 g. Optimised feed was manufactured and compared to commercially available reference feed with respect to feeding intake, feed efficiency, the specific growth rate of fingerlings of Tilapia sp, and, most important, zootechnical parameters. With a fish survival rate of 100% calculated feed conversion index for the formulated feed was 2.7.

Keywords: conversion index, fish waste, formulated feed, tomato waste

Procedia PDF Downloads 151

Authors: Dammar Bahadur Adhikari

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Mathematics teaching begins with human civilization. The rular used to choose mathematician as prime adviser in many tribes and country. Mathematics was powerful tool for understanding economial situation and strength of rular. In ancient Nepal teaching of mathematics starts with informal education provided by religious leaders there after in modern education system seems to follow the world’s educational system. The aim of this paper is to present a brief historical background of the Nepalese mathematicians up to nineteenth century and highlight the transformation in mathematical science in the line with modern world. Secondary data and formal papers and informal publications were studied to explore the present situation of education. The study concluded that there is remarcable change in quality of education and there are sufficient human powers in the mathematical sciences in Nepal.

Keywords: human development, mathematics, Nepal, science, traditional

Procedia PDF Downloads 387

Authors: Abanob Nady Wasef Moawed

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In more complicated systems, inclusive of automotive gearboxes, a rigorous remedy of the data is essential because there are several transferring elements (gears, bearings, shafts, and many others.), and in this way, there are numerous viable sources of mistakes and also noise. The fundamental goal of these elements are the detection of damage in car gearbox. The detection strategies used are the wavelet technique, the bispectrum, advanced filtering techniques (selective filtering) of vibrational alerts and mathematical morphology. Gearbox vibration assessments were achieved (gearboxes in proper circumstance and with defects) of a manufacturing line of a huge car assembler. The vibration indicators have acquired the use of five accelerometers in distinct positions of the sample. The effects acquired using the kurtosis, bispectrum, wavelet and mathematical morphology confirmed that it's far possible to identify the lifestyles of defects in automobile gearboxes.

Keywords: 3D-shaped electronics, electronic components, thermoforming, component positioningautomotive gearbox, mathematical morphology, wavelet, bispectrum

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Authors: S. Jayasinghe, R. B. N. Dissanayake

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Optimization modelling together with the Network models and Linear Programming techniques is a powerful tool in problem solving and decision making in real world applications. This study developed a mathematical model to optimize the net profit by minimizing the transportation cost. This model focuses the transportation among decentralized production plants to a centralized distribution centre and then the distribution among island wide agencies considering the customer satisfaction as a requirement. This company produces basically 9 types of food items with 82 different varieties and 4 types of non-food items with 34 different varieties. Among 6 production plants, 4 were located near the city of Mawanella and the other 2 were located in Galewala and Anuradhapura cities which are 80 km and 150 km away from Mawanella respectively. The warehouse located in the Mawanella was the main production plant and also the only distribution plant. This plant distributes manufactured products to 39 agencies island-wide. The average values and average amount of the goods for 6 consecutive months from May 2013 to October 2013 were collected and then average demand values were calculated. The following constraints are used as the necessary requirement to satisfy the optimum condition of the model; there was one source, 39 destinations and supply and demand for all the agencies are equal. Using transport cost for a kilometer, total transport cost was calculated. Then the model was formulated using distance and flow of the distribution. Network optimization and linear programming techniques were used to originate the model while excel solver is used in solving. Results showed that company requires total transport cost of Rs. 146, 943, 034.50 to fulfil the customers’ requirement for a month. This is very much less when compared with data without using the model. Model also proved that company can reduce their transportation cost by 6% when distributing to island-wide customers. Company generally satisfies their customers’ requirements by 85%. This satisfaction can be increased up to 97% by using this model. Therefore this model can be used by other similar companies in order to reduce the transportation cost.

Keywords: mathematical model, network optimization, linear programming

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Authors: Ka C. Lam, Oluwafunmibi S. Idowu

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Uncertainty in cost is a major factor affecting performance of construction projects. To our knowledge, several conceptual cost models have been developed with varying degrees of accuracy. Incorporating conceptual quantities into conceptual cost models could improve the accuracy of early predesign cost estimates. Hence, the development of quantity models for estimating conceptual quantities of framed reinforced concrete structures using supervised machine learning is the aim of the current research. Using measured quantities of structural elements and design variables such as live loads and soil bearing pressures, response and predictor variables were defined and used for constructing conceptual quantities models. Twenty-four models were developed for comparison using a combination of non-parametric support vector regression, linear regression, and bootstrap resampling techniques. R programming language was used for data analysis and model implementation. Gross soil bearing pressure and gross floor loading were discovered to have a major influence on the quantities of concrete and reinforcement used for foundations. Building footprint and gross floor loading had a similar influence on beams and slabs. Future research could explore the modelling of other conceptual quantities for walls, finishes, and services using machine learning techniques. Estimation of conceptual quantities would assist construction planners in early resource planning and enable detailed performance evaluation of early cost predictions.

Keywords: bootstrapping, conceptual quantities, modelling, reinforced concrete, support vector regression

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Authors: Shashi Kant Mishra

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In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPEC). We establish necessary and sufficient optimality conditions for the SIMPEC, using convexificators. We study the Wolfe type dual problem for the SIMPEC under the ∂∗convexity assumptions. A Mond-Weir type dual problem is also formulated and studied for the SIMPEC under the ∂∗-convexity, ∂∗-pseudoconvexity and ∂∗quasiconvexity assumptions. Weak duality theorems are established to relate the SIMPEC and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification (GS-ACQ).

Keywords: mathematical programming problems with equilibrium constraints, optimality conditions, semi-infinite programming, convexificators

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Authors: Taehan Bae

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In this paper, a class of length-biased Weibull mixtures is presented to model loss severity data. The proposed model generalizes the Erlang mixtures with the common scale parameter, and it shares many important modelling features, such as flexibility to fit various data distribution shapes and weak-denseness in the class of positive continuous distributions, with the Erlang mixtures. We show that the asymptotic tail estimate of the length-biased Weibull mixture is Weibull-type, which makes the model effective to fit loss severity data with heavy-tailed observations. A method of statistical estimation is discussed with applications on real catastrophic loss data sets.

Keywords: Erlang mixture, length-biased distribution, transformed gamma distribution, asymptotic tail estimate, EM algorithm, expectation-maximization algorithm

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Authors: Fatemeh Yazdanmehr, Iulian Nistor

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The scope of the current study is the evaluation of the electric field effect on electrostatic desalting mathematical modeling with laboratory data. This research study was focused on developing a model for an existing operation desalting unit of one of the Iranian heavy oil field with a 75 MBPD production capacity. The high temperature of inlet oil to dehydration unit reduces the oil recovery, so the mathematical modeling of desalter operation parameters is very significant. The existing production unit operating data has been used for the accuracy of the mathematical desalting plant model. The inlet oil temperature to desalter was decreased from 110 to 80°C, and the desalted electrical field was increased from 0.75 to 2.5 Kv/cm. The model result shows that the desalter parameter changes meet the water-oil specification and also the oil production and consequently annual income is increased. In addition to that, changing desalter operation conditions reduces environmental footprint because of flare gas reduction. Following to specify the accuracy of selected electrostatic desalter electrical field, laboratory data has been used. Experimental data are used to ensure the effect of electrical field change on desalter. Therefore, the lab test is done on a crude oil sample. The results include the dehydration efficiency in the presence of a demulsifier and under electrical field (0.75 Kv) conditions at various temperatures. Comparing lab experimental and electrostatic desalter mathematical model results shows 1-3 percent acceptable error which confirms the validity of desalter specification and operation conditions changes.

Keywords: desalter, electrical field, demulsification, mathematical modeling, water-oil separation

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Authors: M. A. Khanday, Aasma Rafiq, Khalid Nazir

Abstract:

This paper is an attempt to establish the mathematical models to understand the distribution of drug administration in the human body through oral and intravenous routes. Three models were formulated based on diffusion process using Fick’s principle and the law of mass action. The rate constants governing the law of mass action were used on the basis of the drug efficacy at different interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the ordinary differential equations concerning the rate of change of concentration in different compartments viz. blood and tissue medium. The drug concentration in the different compartments has been computed using numerical parameters. The results illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the results that the drug concentration decreases in the first compartment and gradually increases in other subsequent compartments.

Keywords: Laplace transform, diffusion, eigenvalue method, mathematical model

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Authors: Serhat Tuzun, Tufan Demirel

Abstract:

Multi-Criteria Decision Making (MCDM) is the modelling of real-life to solve problems we encounter. It is a discipline that aids decision makers who are faced with conflicting alternatives to make an optimal decision. MCDM problems can be classified into two main categories: Multi-Attribute Decision Making (MADM) and Multi-Objective Decision Making (MODM), based on the different purposes and different data types. Although various MADM techniques were developed for the problems encountered, their methodology is limited in modelling real-life. Moreover, objective results are hard to obtain, and the findings are generally derived from subjective data. Although, new and modified techniques are developed by presenting new approaches such as fuzzy logic; comprehensive techniques, even though they are better in modelling real-life, could not find a place in real world applications for being hard to apply due to its complex structure. These constraints restrict the development of MADM. This study aims to conduct a comprehensive analysis of preference methods in MADM and propose an approach based on information. For this purpose, a detailed literature review has been conducted, current approaches with their advantages and disadvantages have been analyzed. Then, the approach has been introduced. In this approach, performance values of the criteria are calculated in two steps: first by determining the distribution of each attribute and standardizing them, then calculating the information of each attribute as informational energy.

Keywords: literature review, multi-attribute decision making, operations research, preference method, informational energy

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