Search results for: mathematical games

Authors: Shrikant Ghadage

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Study of shock waves generated in the Scramjet engine is typically restricted to pressure, temperature, density, entropy and Mach number variation across the shock wave. The present work discusses the impact of inlet shock wave angles on the specific impulse of the Scramjet engine. A mathematical analysis has done for the isentropic hypersonic flow of air flowing through a Scramjet with hydrogen fuel at an altitude of 30 km. Analysis has been done in order to get optimum shock wave angle to achieve maximum impulse. Since external drag has excluded from the analysis, the losses due to friction are not considered for the present analysis. When Mach number of the airflow at the entry of the nozzle reaches unity, then that flow is choked. This condition puts limitations on increasing the inlet shock wave angle. As inlet shock wave angle increases, speed of the flow entering into the nozzle decreases, which results in an increase in the specific impulse of the engine. When the speed of the flow at the entry of the nozzle reduces below sonic speed, then there is no further increase in the specific impulse of the engine. Here the Conclusion is the thrust and specific impulse of a scramjet engine, which increases gradually with an increase in inlet shock wave angle up to the condition when airflow speed reaches sonic velocity at the exit of the combustor. In addition to that, variation in drag force at the inlet of the scramjet and variation in hypersonic flow conditions at every stage of the scramjet also studied in order to understand variation on flow characteristics with respect to flow deflection angle. Essentially, it helps in designing inlet profile for the Scramjet engine to achieve optimum specific impulse.

Keywords: hypersonic flow, scramjet, shock waves, specific impulse, mathematical analysis

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Authors: Hui Fang Huang Su, Leanne Lai, Pei-Fen Li, Mei-Hwei Ho, Yu-Wen Chiu

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This study aimed to provide a practical, systematic, and comprehensive intervention for children with Autism Spectrum Disorder (ASD). A pilot study of quasi-experimental pre-post intervention with control group design was conducted to evaluate if the mathematical intervention (Project MIND - Math Is Not Difficult) increases the math comprehension of children with ASD Children with ASD in the primary grades (K-1, 2) participated in math interventions to enhance their math comprehension and cognitive ability. The Bracken basic concept scale was used to evaluate subjects’ language skills, cognitive development, and school readiness. The study found that our systemic interventions of Project MIND significantly improved the mathematical and cognitive abilities in children with autism. The results of this study may lead to a major change in effective and adequate health care services for children with ASD and their families. All statistical analyses were performed with the IBM SPSS Statistics Version 25 for Windows. The significant level was set at 0.05 P-value.

Keywords: autism, mathematics, technology, family

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Authors: Mohamed El Hattab

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The Supercritical carbon dioxide (SFE) and the focused microwave-assisted hydrodistillation (FMAHD) were employed to isolate the volatile fraction of the brown alga Dictyopteris membranacea from the crude extract. The volatiles fractions obtained were analyzed by GC/MS. The major compounds in this case: dictyopterene A, 6-butylcyclohepta-1,4-diene, Undec-1-en-3-one, Undeca-1,4-dien-3-one, (3-oxoundec-4-enyl) sulphur, tetradecanoic acid, hexadecanoic acid, 3-hexyl-4,5-dithia-cycloheptanone and albicanol (this later is present only in the FMAHD oil) are identified by comparing their mass spectra with those reported on the commercial MS data base and also on our previously work. A kinetic study realized on both extraction processes and followed by an external standard quantification has allowed the study of the mass percent evolution of the major compounds in the two oils, an empirical mathematical modelling was used to describe their kinetic extraction.

Keywords: dictyopteris membranacea, extraction techniques, mathematical modeling, volatile oils

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Authors: Alexander I. Dovgyallo, Evgeniy A. Zinoviev, Svetlana O. Nekrasova

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The most of works applied for the pulse tube converters contain the workflow description implemented through the use of mathematical models on stationary modes. However, the study of the thermoacoustic systems unsteady behavior in the start, stop, and acoustic load changes modes is in the particular interest. The aim of the present study was to develop a mathematical thermal excitation model of acoustic oscillations in pulse tube engine (PTE) as a small-scale scheme of pulse tube engine operating at atmospheric air. Unlike some previous works this standing wave configuration is a fully closed system. The improvements over previous mathematical models are the following: the model allows specifying any values of porosity for regenerator, takes into account the piston weight and the friction in the cylinder and piston unit, and determines the operating frequency. The numerical method is based on the relation equations between the pressure and volume velocity variables at the ends of each element of PTE which is recorded through the appropriate transformation matrix. A solution demonstrates that the PTE operation frequency is the complex value, and it depends on the piston mass and the dynamic friction due to its movement in the cylinder. On the basis of the determined frequency thermoacoustically induced heat transport and generation of acoustic power equations were solved for channel with temperature gradient on its ends. The results of numerical simulation demonstrate the features of the initialization process of oscillation and show that that generated acoustic power more than power on the steady mode in a factor of 3…4. But doesn`t mean the possibility of its further continuous utilizing due to its existence only in transient mode which lasts only for a 30-40 sec. The experiments were carried out on small-scale PTE. The results shows that the value of acoustic power is in the range of 0.7..1.05 W for the defined frequency range f = 13..18 Hz and pressure amplitudes 11..12 kPa. These experimental data are satisfactorily correlated with the numerical modeling results. The mathematical model can be straightforwardly applied for the thermoacoustic devices with variable temperatures of thermal reservoirs and variable transduction loads which are expected to occur in practical implementations of portable thermoacoustic engines.

Keywords: nonlinear processes, pulse tube engine, thermal excitation, standing wave

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Authors: Shokofeh Ebrtahimi

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Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G.Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena.[1] The pioneers of the chemical graph theory are Alexandru Balaban, Ante Graovac, Ivan Gutman, Haruo Hosoya, Milan Randić and Nenad TrinajstićLet G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new program for computing the detour index of molecular graphs of nanotubes by heptagons is determineded. Some Conjectures about detour index of Molecular graphs of nanotubes is included.

Keywords: chemical graph, detour matrix, Detour index, carbon nanotube

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Authors: Satya P. Dubey, Hrushikesh A Abhyankar, Veronica Marchante, James L. Brighton, Björn Bergmann

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Aims: To develop a mathematical model that simulates the ROP of PLA taking into account the effect of alternative energy to be implemented in a continuous reactive extrusion production process of PLA. Introduction: The production of large amount of waste is one of the major challenges at the present time, and polymers represent 70% of global waste. PLA has emerged as a promising polymer as it is compostable, biodegradable thermoplastic polymer made from renewable sources. However, the main limitation for the application of PLA is the traces of toxic metal catalyst in the final product. Thus, a safe and efficient production process needs to be developed to avoid the potential hazards and toxicity. It has been found that alternative energy sources (LASER, ultrasounds, microwaves) could be a prominent option to facilitate the ROP of PLA via continuous reactive extrusion. This process may result in complete extraction of the metal catalysts and facilitate less active organic catalysts. Methodology: Initial investigation were performed using the data available in literature for the reaction mechanism of ROP of PLA based on conventional metal catalyst stannous octoate. A mathematical model has been developed by considering significant parameters such as different initial concentration ratio of catalyst, co-catalyst and impurity. Effects of temperature variation and alternative energies have been implemented in the model. Results: The validation of the mathematical model has been made by using data from literature as well as actual experiments. Validation of the model including alternative energies is in progress based on experimental data for partners of the InnoREX project consortium. Conclusion: The model developed reproduces accurately the polymerisation reaction when applying alternative energy. Alternative energies have a great positive effect to increase the conversion and molecular weight of the PLA. This model could be very useful tool to complement Ludovic® software to predict the large scale production process when using reactive extrusion.

Keywords: polymer, poly-lactic acid (PLA), ring opening polymerization (ROP), metal-catalyst, bio-degradable, renewable source, alternative energy (AE)

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Authors: Yassir I. Dinar

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We computed the weights of the adjoint action of distinguished sl2-triples in Lie algebra of type Dn using mathematical induction.

Keywords: lie algebra, root systems, representation theory, nilpotent orbits

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Authors: U. Harel, E. Carmeli

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The Purpose was to measure differences in activity patterns between major league adult and U-21 soccer players. Four U-21 players and four adult team players were evaluated using a repeated measures technique. All eight players were affiliated with the Maccabi Haifa soccer club from the Israeli professional and U-21major leagues, depending on the player’s age. GPS sensors were attached to the players during five consecutive games to identify patterns regarding running distance and speed according to the field positions. There was no significant difference in the total running distances covered by two age groups. When measuring running speed, an advantage was observed in the adult group when comparing two players from different age groups that played the same position. Differences in activity patterns were evident between adult and U-21 major league soccer players. Furthermore, differences in within group activity pattern emerged between the positions under investigation. These findings provide valuable knowledge that may serve the principle of training specificity.

Keywords: physical fitness, soccer, positional differences, GPS, training specificity

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Authors: Ka C. Lam, Oluwafunmibi S. Idowu

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Building girth is important in building economics and mostly used in quantities take-off of various cost items. Literature suggests that the use of conceptual quantities can improve the accuracy of cost models. Girth or perimeter of a building can be used to estimate conceptual quantities. Hence, the current paper aims to model the perimeter-area function of buildings shapes for use at the conceptual design stage. A detailed literature review on existing building shape indexes was carried out. An empirical approach was used to study the relationship between area and the shortest length of a four-sided orthogonal polygon. Finally, a mathematical approach was used to establish the observed relationships. The empirical results obtained were in agreement with the mathematical model developed. A new equation termed “conceptual perimeter equation” is proposed. The equation can be used to estimate building envelope quantities such as external wall area, external finishing area and scaffolding area before sketch or detailed drawings are prepared.

Keywords: building envelope, building shape index, conceptual quantities, cost modelling, girth

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Authors: Arpan Dwivedi, Yogesh Pahariya

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In this paper, optimal design of hybrid standalone power supply system (SAPS) is done for off grid applications in remote areas where transmission of power is difficult. The hybrid SAPS system uses two primary energy sources, wind and solar, and in addition to these diesel generator is also connected to meet the load demand in case of failure of wind and solar system. This paper presents mathematical modeling of 1.4 MW hybrid SAPS system for rural electrification. This paper firstly focuses on mathematical modeling of PV module connected in a string, secondly focuses on modeling of permanent magnet wind turbine generator (PMWTG). The hybrid controller is also designed for selection of power from the source available as per the load demand. The power output of hybrid SAPS system is analyzed for meeting load demands at urban as well as for rural areas.

Keywords: SAPS, DG, PMWTG, rural area, off-grid, PV module

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Authors: Hakan Bozdoğan

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The goal of this paper is to evaluate the species richness, diversity and structure of in different habitats in the Kahramanmaraş Province in Turkey by using a mathematical program called as Geo-Gebra Software. The Ascalaphidae family comprises the most visually remarkable members of the order Neuroptera due to large dimensions, aerial predatory behaviour and dragonfly-like (or even butterfly-like) habits, allowing an immediate recognition also for occasional observers. Otherwise, they are one of the more poorly known families of the order in respect to biology, ecology and especially larval morphology. This discrepancy appears particularly noteworthy considering that it is a fairly large family (ca. 430 species) widely distributed in tropical and temperate areas of the World. The use of Dynamic Geometry, Analytical Softwares provides researchers a great way of visualising mathematical objects and encourage them to carry out tasks to interact with such objects and add to support of their researching. In this study we implemented; Circle with Center Through Point, Perpendicular Line, Vectors and Rays, Segments and Locus to elucidate the ecological and habitat behaviours of Butterfly-like lacewings in an analytical plane by using Geo-Gebra.

Keywords: neuroptera, Ascalaphidae, geo-gebra software, habitat selectivity

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Authors: Vimuckthi Charika Wickramaratne, Prasansha Kumari

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Sport tourism refers to travel which involves either observing or participating in a sporting event apart from their usual environment. Sport tourism in a fast growing sector of the Sri Lankan travelling industry since Cricket are more popular sport game in the country. This study intends to analyze the impact of these popular sport events for creating and developing small scale business in the country. Primary data gathered from 100 small entrepreneurs around Keththarama Cricket Ground in Sri Lanka. Collected data analyzed using descriptive research methods. The study revealed that local and international visitors for cricket games had impacted on small scale business activities such as retail, handicraft, transport, vehicle parking, small restaurant, hotels, foods and beverage industry. In addition, it was identified that these type of small business are sessional income generating activities for the short period.

Keywords: sport tourism, small scale business, cricket, entrepreneurs

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Authors: Easa Ali Abbasi, Akbar Allahverdizadeh, Reza Jahangiri, Behnam Dadashzadeh

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Electrical current measurement is a suitable method for the performance determination of electrical devices. There are two contact and noncontact methods in this measuring process. Contact method has some disadvantages like having direct connection with wire which may endamage the system. Thus, in this paper, a bimorph piezoelectric cantilever beam which has a permanent magnet on its free end is used to measure electrical current in a noncontact way. In mathematical modeling, based on Galerkin method, the governing equation of the cantilever beam is solved, and the equation presenting the relation between applied force and beam’s output voltage is presented. Magnetic force resulting from current carrying wire is considered as the external excitation force of the system. The results are compared with other references in order to demonstrate the accuracy of the mathematical model. Finally, the effects of geometric parameters on the output voltage and natural frequency are presented.

Keywords: cantilever beam, electrical current measurement, forced excitation, piezoelectric

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Authors: Mingzhu Lyu, Runlei Ren, Xinyu Dai, Jiaxuan Pi, Kanghua Li

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The study of video game policy in China has been divided into two branches: "pedagogy" and "game industry". The binary perspective of policy reveals the "contradictory" side of policy performance. Based on this suspicion, this paper constructs a three-dimensional sequence of time, content and institutions of game policy, and establishes the "contradictory" aspects of policy performance between 1949 and 2019. A central-level database of game policies, clarifying that our game policies follow a shift from reactive response to proactive guidance, stigmatization and de-stigmatization, the evolutionary logic. The study found that the central government has always maintained a strict requirement and prudent guidance for game policy, and the deep contradictions in game policy stem from the essential conflict between the natural amusement of games and the seriousness of the educational system, and the Chinese government's use of the understanding of the public and private domains and the Managing of the conflict.

Keywords: game industry, gaming policy, public domain, private domain

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Authors: Petr Květon, Martin Jelínek

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We try to identify the role of various aspects of parenting style in the phenomenon of videogame playing addiction. Relevant self-report questionnaires were part of a wider set of methods focused on the constructs related to videogame playing. The battery of methods was administered in school settings in paper and pencil form. The research sample consisted of 333 (166 males, 167 females) elementary and high school students at the age between 10 and 19 years (m=14.98, sd=1.77). Using stepwise regression analysis, we assessed the influence of demographic variables (gender and age) and parenting styles. Age and gender together explained 26.3% of game addiction variance (F(2,330)=58.81, p<.01). By adding four aspect of parenting styles (inconsistency, involvement, control, and warmth) another 10.2% of variance was explained (∆F(4,326)=13.09, p<.01). The significant predictor was gender of the respondent, where males scored higher on game addiction scale (B=0.70, p<.01), age (β=-0.18, p<.01), where younger children showed higher level of addiction, and parental inconsistency (β=0.30, p<.01), where the higher the inconsistency in upbringing, the more developed game playing addiction.

Keywords: gender, parenting styles, video games, addiction

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Authors: Yunusa Aliyu Hadejia

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Cholera is a gastrointestinal disease caused by a bacterium called Vibrio Cholerae which spread as a result of eating food or drinking water contaminated with feaces from an infected person. In this work we proposed and analyzed the impact of isolating infected people and give them therapeutic treatment, the specific objectives of the research was to formulate a mathematical model of cholera transmission incorporating treatment class, to make analysis on stability of equilibrium points of the model, positivity and boundedness was shown to ensure that the model has a biological meaning, the basic reproduction number was derived by next generation matrix approach. The result of stability analysis show that the Disease free equilibrium was both locally and globally asymptotically stable when R_0< 1 while endemic equilibrium has locally asymptotically stable when R_0> 1. Sensitivity analysis was perform to determine the contribution of each parameter to the basic reproduction number. Numerical simulation was carried out to show the impact of the model parameters using MAT Lab Software.

Keywords: mathematical model, treatment, stability, sensitivity

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Authors: D. Kumar, S. Kumar, A. G. Memon, R. A. Memon, K. Harijan

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A considerable amount of energy is usually lost due to compression of insulation in Heating, ventilation, and air conditioning (HVAC) duct. In this paper, the economic impact of compression of insulation is estimated. Relevant mathematical models were used to estimate the optimal thickness at the points of compression. Furthermore, the payback period is calculated for the optimal thickness at the critical parts of supply air duct (SAD) and return air duct (RAD) considering natural gas (NG) and liquefied petroleum gas (LPG) as fuels for chillier operation. The mathematical model is developed using preliminary data obtained for an HVAC system of a pharmaceutical company. The higher heat gain and cooling loss, due to compression of thermal insulation, is estimated using relevant heat transfer equations. The results reveal that maximum energy savings (ES) in SAD is 34.5 and 40%, while in RAD is 22.9% and 29% for NG and LPG, respectively. Moreover, the minimum payback period (PP) for SAD is 2 and 1.6years, while in RAD is 4.3 and 2.7years for NG and LPG, respectively. The optimum insulation thickness (OIT) corresponding to maximum ES and minimum PP is estimated to be 35 and 42mm for SAD, while 30 and 38mm for RAD in case of NG and LPG, respectively.

Keywords: optimum insulation thickness, life cycle cost analysis, payback period, HVAC system

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Authors: Bruno Biagianti, Angela Tseng, Kathy Wannaviroj, Allison Corlett, Megan DuBois, Kyu Lee, Suma Jacob

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Background: ASD is characterized by pervasive Sensory Processing Abnormalities (SPA) and social cognitive deficits that persist throughout the course of the illness and have been linked to functional abnormalities in specific neural systems that underlie the perception, processing, and representation of sensory information. SPA and social cognitive deficits are associated with difficulties in interpersonal relationships, poor development of social skills, reduced social interactions and lower academic performance. Importantly, they can hamper the effects of established evidence-based psychological treatments—including PEERS (Program for the Education and Enrichment of Relationship Skills), a parent/caregiver-assisted, 16-weeks social skills intervention—which nonetheless requires a functional brain capable of assimilating and retaining information and skills. As a matter of fact, some adolescents benefit from PEERS more than others, calling for strategies to increase treatment response rates. Objective: We will present interim data on CICADAS (Care Improving Cognition for ADolescents on the Autism Spectrum)—a clinician-assisted, closed-loop technology mobile application for adolescents with ASD. Via ten mobile assessments, CICADAS captures data on sensory processing abnormalities and associated cognitive deficits. These data populate a machine learning algorithm that tailors the delivery of ten neuroplasticity-based social cognitive training (NB-SCT) exercises targeting sensory processing abnormalities. Methods: In collaboration with the Autism Spectrum and Neurodevelopmental Disorders Clinic at the University of Minnesota, we conducted a fully remote, three-arm, randomized crossover trial with adolescents with ASD to document the acceptability of CICADAS and evaluate its potential as a stand-alone treatment or as a treatment enhancer of PEERS. Twenty-four adolescents with ASD (ages 11-18) have been initially randomized to 16 weeks of PEERS + CICADAS (Arm A) vs. 16 weeks of PEERS + computer games vs. 16 weeks of CICADAS alone (Arm C). After 16 weeks, the full battery of assessments has been remotely administered. Results: We have evaluated the acceptability of CICADAS by examining adherence rates, engagement patterns, and exit survey data. We found that: 1) CICADAS is able to serve as a treatment enhancer for PEERS, inducing greater improvements in sensory processing, cognition, symptom reduction, social skills and behaviors, as well as the quality of life compared to computer games; 2) the concurrent delivery of PEERS and CICADAS induces greater improvements in study outcomes compared to CICADAS only. Conclusion: While preliminary, our results indicate that the individualized assessment and treatment approach designed in CICADAS seems effective in inducing adaptive long-term learning about social-emotional events. CICADAS-induced enhancement of processing and cognition facilitates the application of PEERS skills in the environment of adolescents with ASD, thus improving their real-world functioning.

Keywords: ASD, social skills, cognitive training, mobile app

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Authors: Wenzhe Li, Xiaoyu Ying, Grace Ding

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Architecture plane form is an important consideration in the design of green buildings due to its significant impact on energy performance. The most effective method to consider energy performance in the early design stages is parametric modelling. This paper presents a methodology to program plane forms using MATLAB language, generating 16 kinds of plane forms by changing four designed parameters. DesignBuilder (an energy consumption simulation software) was proposed to simulate the energy consumption of the generated planes. A regression mathematical model was established to study the relationship between the plane forms and their energy consumption. The main finding of the study suggested that there was a cubic function relationship between the depth-ratio of U-shaped buildings and energy consumption, and there is also a cubic function relationship between the width-ratio and energy consumption. In the design, the depth-ratio of U-shaped buildings should not be less than 2.5, and the width-ratio should not be less than 2.

Keywords: graphic parameterization, green building design, mathematical model, plane form

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Authors: Aleksandar Hatzivelkos

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The term ”compromise” is mostly used casually within the social choice theory. It is usually used as a mere result of the social choice function, and this omits its deeper meaning and ramifications. This paper is based on a mathematical model for the description of a compromise as a version of the Sorites paradox. It introduces a formal definition of d-measure of divergence from a compromise and models a notion of compromise that is often used only colloquially. Such a model for vagueness phenomenon, which lies at the core of the notion of compromise enables the introduction of new mathematical structures. In order to maximize compromise, different methods can be used. In this paper, we explore properties of a social welfare function TdM (from Total d-Measure), which is defined as a function which minimizes the total sum of d-measures of divergence over all possible linear orderings. We prove that TdM satisfy strict Pareto principle and behaves well asymptotically. Furthermore, we show that for certain domain restrictions, TdM satisfy positive responsiveness and IIIA (intense independence of irrelevant alternatives) thus being equivalent to Borda count on such domain restriction. This result gives new opportunities in social choice, especially when there is an emphasis on compromise in the decision-making process.

Keywords: borda count, compromise, measure of divergence, minimization

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Authors: Thomas Arink, Isam Janajreh

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The petroleum industry generates significant amounts of waste in the form of drill cuttings, contaminated soil and oily sludge. Drill cuttings are a product of the off-shore drilling rigs, containing wet soil and total petroleum hydrocarbons (TPH). Contaminated soil comes from different on-shore sites and also contains TPH. The oily sludge is mainly residue or tank bottom sludge from storage tanks. The two main treatment methods currently used are incineration and thermal desorption (TD). Thermal desorption is a method where the waste material is heated to 450ºC in an anaerobic environment to release volatiles, the condensed volatiles can be used as a liquid fuel. For the thermal desorption unit dry contaminated soil is mixed with moist drill cuttings to generate a suitable mixture. By thermo gravimetric analysis (TGA) of the TD feedstock it was found that less than 50% of the TPH are released, the discharged material is stored in landfill. This study proposes co-gasification of petroleum waste with waste tires as an alternative to thermal desorption. Co-gasification with a high-calorific material is necessary since the petroleum waste consists of more than 60 wt% ash (soil/sand), causing its calorific value to be too low for gasification. Since the gasification process occurs at 900ºC and higher, close to 100% of the TPH can be released, according to the TGA. This work consists of three parts: 1. a mathematical gasification model, 2. a reactive flow CFD model and 3. experimental work on a drop tube reactor. Extensive material characterization was done by means of proximate analysis (TGA), ultimate analysis (CHNOS flash analysis) and calorific value measurements (Bomb calorimeter) for the input parameters of the mathematical and CFD model. The mathematical model is a zero dimensional model based on Gibbs energy minimization together with Lagrange multiplier; it is used to find the product species composition (molar fractions of CO, H2, CH4 etc.) for different tire/petroleum feedstock mixtures and equivalence ratios. The results of the mathematical model act as a reference for the CFD model of the drop-tube reactor. With the CFD model the efficiency and product species composition can be predicted for different mixtures and particle sizes. Finally both models are verified by experiments on a drop tube reactor (1540 mm long, 66 mm inner diameter, 1400 K maximum temperature).

Keywords: computational fluid dynamics (CFD), drop tube reactor, gasification, Gibbs energy minimization, petroleum waste, waste tires

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Authors: Natalia Podkhodova, Olga Sheremeteva, Mariia Soldaeva

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Creating favorable conditions for students’ comprehension of mathematical content is one of the primary problems in teaching mathematics in secondary school. Psychology research has demonstrated that positive comprehension becomes possible when new information becomes part of student’s subjective experience and when linkages between the attributes of notions and various ways of their presentations can be established. The fact of comprehension includes the ability to build a working situational model and thus becomes an important means of solving mathematical problems. The article describes the implementation of a holistic approach to teaching mathematics designed to address the primary challenges of such teaching, specifically, the challenge of students’ comprehension. This approach consists of (1) establishing links between the attributes of a notion: the sense, the meaning, and the term; (2) taking into account the components of student’s subjective experience -emotional and value, contextual, procedural, communicative- during the educational process; (3) links between different ways to present mathematical information; (4) identifying and leveraging the relationships between real, perceptual and conceptual (scientific) mathematical spaces by applying real-life situational modeling. The article describes approaches to the practical use of these foundational concepts. Identifying how proposed methods and technology influence understanding of material used in teaching mathematics was the research’s primary goal. The research included an experiment in which 256 secondary school students took part: 142 in the experimental group and 114 in the control group. All students in these groups had similar levels of achievement in math and studied math under the same curriculum. In the course of the experiment, comprehension of two topics -'Derivative' and 'Trigonometric functions'- was evaluated. Control group participants were taught using traditional methods. Students in the experimental group were taught using the holistic method: under the teacher’s guidance, they carried out problems designed to establish linkages between notion’s characteristics, to convert information from one mode of presentation to another, as well as problems that required the ability to operate with all modes of presentation. The use of the technology that forms inter-subject notions based on linkages between perceptional, real, and conceptual mathematical spaces proved to be of special interest to the students. Results of the experiment were analyzed by presenting students in each of the groups with a final test in each of the studied topics. The test included problems that required building real situational models. Statistical analysis was used to aggregate test results. Pierson criterion was used to reveal the statistical significance of results (pass-fail the modeling test). A significant difference in results was revealed (p < 0.001), which allowed the authors to conclude that students in the study group showed better comprehension of mathematical information than those in the control group. Also, it was revealed (used Student’s t-test) that the students of the experimental group performed reliably (p = 0.0001) more problems in comparison with those in the control group. The results obtained allow us to conclude that increasing comprehension and assimilation of study material took place as a result of applying implemented methods and techniques.

Keywords: comprehension of mathematical content, holistic approach to teaching mathematics in secondary school, subjective experience, technology of the formation of inter-subject notions

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Authors: Ayşegül Çabuk, Mine Işıksal

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Mathematics is a sense-making activity so that it requires meaningful learning. Hence based on this idea, meaningful mathematical connections are necessary to learn mathematics. At that point, the major question has become that which educational methods can provide opportunities to provide mathematical connections and to understand mathematics. The amalgam of reasoning and proof can be the one of the methods that creates opportunities to learn mathematics in a meaningful way. However, even if reasoning and proof should be included from prekindergarten to grade 12, studies in literature generally include secondary school students and pre-service mathematics teachers. With the light of the idea that the amalgam of reasoning and proof has significant effect on middle school students' mathematical learning, this study aims to investigate middle grade students' tendencies while reasoning the correctness of statements related to numbers. The sample included 272 middle grade students, specifically 69 of them were sixth grade students (25.4%), 101 of them were seventh grade students (37.1%) and 102 of them were eighth grade students (37.5%). Data was gathered through an achievement test including 2 essay types of problems about algebra. The answers of two items were analyzed both quantitatively and qualitatively in terms of students' solutions strategies while reasoning the correctness of the statements. Similar on the findings in the literature, most of the students, in all grade levels, used numerical examples to judge the statements. Moreover the results also showed that the majority of these students appear to believe that providing one or more selected examples is sufficient to show the correctness of the statement. Hence based on the findings of the study, even students in earlier ages have proving and reasoning abilities their reasoning's generally based on the empirical evidences. Therefore, it is suggested that examples and example-based reasoning can be a fundamental role on to generate systematical reasoning and proof insight in earlier ages.

Keywords: reasoning, mathematics learning, middle grade students

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Authors: Aiswarya Gopal, Kamal Bijlani, Vinoth Rengaraj, R. Jayakrishnan

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In the business world, the term “startup” is frequently ringing the bell with the high frequency of young ventures. The main dilemma of startups is the unsuccessful management of the unique risks that have to be confronted in the present world of competition and technology. This research work tried to bring out a game based methodology to improve enough real-world experience among entrepreneurs as well as management students to handle risks and challenges in the field. The game will provide experience to the player to overcome challenges like market problems, running out of cash, poor management, and product problems which can be resolved by a proper strategic approach in the entrepreneurship world. The proposed serious game works on the life cycle of a new software enterprise where the entrepreneur moves from the planning stage to secured financial stage, laying down the basic business structure, and initiates the operations ensuring the increment in confidence level of the player.

Keywords: business model, game based learning, poor management, start up

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Authors: Aneta Oblouková, Eva Vítková

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The article deals with the issue of water and sewerage charge rate prices in the Czech Republic. The research is specifically focused on the analysis of the development of the average prices of water and sewerage charge rate in the Czech Republic in the years 1994-2021 and on the validation of the chosen methodology relevant for the prediction of the development of the average prices of water and sewerage charge rate in the Czech Republic. The research is based on data collection. The data for this research was obtained from the Czech Statistical Office. The aim of the paper is to validate the relevance of the mathematical linear trend estimate technique for the calculation of the predicted average prices of water and sewerage charge rates. The real values of the average prices of water and sewerage charge rates in the Czech Republic in the years 1994-2018 were obtained from the Czech Statistical Office and were converted into a mathematical equation. The same type of real data was obtained from the Czech Statistical Office for the years 2019-2021. Prediction of the average prices of water and sewerage charge rates in the Czech Republic in the years 2019-2021 were also calculated using a chosen method -a linear trend estimation technique. The values obtained from the Czech Statistical Office and the values calculated using the chosen methodology were subsequently compared. The research result is a validation of the chosen mathematical technique to be a suitable technique for this research.

Keywords: Czech Republic, linear trend estimation, price prediction, water and sewerage charge rate

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Authors: Jiahui Song

Abstract:

In order to predict or explain a complicated biological process, it is important first to construct mathematical models that can be used to yield analytical solutions. Through numerical simulation, mathematical model results can be used to test scenarios that might not be easily attained in a laboratory experiment, or to predict parameters or phenomena. High-intensity, nanosecond pulse electroporation has been a recent development in bioelectrics. The dynamic pore model can be achieved by including a dynamic aspect and a dependence on the pore population density into pore formation energy equation to analyze and predict such electroporation effects. For greater accuracy, with inclusion of atomistic details, molecular dynamics (MD) simulations were also carried out during this study. Besides inducing pores in cells, external voltages could also be used in principle to modulate action potential generation in nerves. This could have an application in electrically controlled ‘pain management’. Also a simple model-based rate equation treatment of the various cellular bio-chemical processes has been used to predict the pulse number dependent cell survival trends.

Keywords: model, high-intensity, nanosecond, bioelectrics

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Authors: Linda A. O’Higgins, Astrid Wingler, Jorge Oliveira

Abstract:

The growth of Chlorella vulgaris was characterized as a function of irradiance in a laboratory turbidostat (1 L) and compared to batch growth in sunlit modules (5–25 L) of the commercial Phytobag photobioreactor. The effects of variable sunlight and culture density were deconvoluted by a mathematical model. The analysis showed that algal growth was light-limited due to shading by external construction elements and due to light attenuation within the algal bags. The model was also used to predict maximum biomass productivity. The manipulative experiments and the model predictions were confronted with data from a production season of a 10m2 pilot-scale photobioreactor, Phytobag (10,000 L). The analysis confirmed light limitation in all three photobioreactors. An additional limitation of biomass productivity was caused by the nitrogen starvation that was used to induce lipid accumulation. Reduction of shading and separation of biomass and lipid production are proposed for future optimization.

Keywords: microalgae, batch cultivation, Chlorella vulgaris, Mathematical model, photobioreactor, scale-up

Procedia PDF Downloads 87

Authors: Muhammad Luqman, Yusuf Kurniawan

Abstract:

S-Boxes is one of the linear parts of the cryptographic algorithm. The existence of S-Box in the cryptographic algorithm is needed to maintain non-linearity of the algorithm. Nowadays, modern cryptographic algorithms use an S-Box as a part of algorithm process. Despite the fact that several cryptographic algorithms today reuse theoretically secure and carefully constructed S-Boxes, there is an evaluation characteristic that can measure security properties of S-Boxes and hence the corresponding primitives. Analysis of an S-Box usually is done using manual mathematics calculation. Several S-Boxes are presented as a Truth Table without any mathematical background algorithm. Then, it’s rather difficult to determine the strength of Truth Table S-Box without a mathematical algorithm. A comprehensive analysis should be applied to the Truth Table S-Box to determine the characteristic. Several important characteristics should be owned by the S-Boxes, they are Nonlinearity, Balancedness, Algebraic degree, LAT, DAT, differential delta uniformity, correlation immunity and global avalanche criterion. Then, a comprehensive tool will be present to automatically calculate the characteristics of S-Boxes and determine the strength of S-Box. Comprehensive analysis is done on a deterministic process to produce a sequence of S-Boxes characteristic and give advice for a better S-Box construction.

Keywords: cryptographic properties, Truth Table S-Boxes, S-Boxes characteristic, deterministic process

Procedia PDF Downloads 345

Authors: N. Alias, W. Z. W. Muhammad, M. N. M. Ibrahim, M. Mohamed, H. F. S. Saipol, U. N. Z. Ariffin, N. A. Zakaria, M. S. Z. Suardi

Abstract:

This paper presents the performance comparison of some computation software for solving the boundary element method (BEM). BEM formulation is the numerical technique and high potential for solving the advance mathematical modeling to predict the production of oil well in arbitrarily shaped based on multiple leases reservoir. The limitation of data validation for ensuring that a program meets the accuracy of the mathematical modeling is considered as the research motivation of this paper. Thus, based on this limitation, there are three steps involved to validate the accuracy of the oil production simulation process. In the first step, identify the mathematical modeling based on partial differential equation (PDE) with Poisson-elliptic type to perform the BEM discretization. In the second step, implement the simulation of the 2D BEM discretization using COMSOL Multiphysic and MATLAB programming languages. In the last step, analyze the numerical performance indicators for both programming languages by using the validation of Fortran programming. The performance comparisons of numerical analysis are investigated in terms of percentage error, comparison graph and 2D visualization of pressure on oil production of multiple leases reservoir. According to the performance comparison, the structured programming in Fortran programming is the alternative software for implementing the accurate numerical simulation of BEM. As a conclusion, high-level language for numerical computation and numerical performance evaluation are satisfied to prove that Fortran is well suited for capturing the visualization of the production of oil well in arbitrarily shaped.

Keywords: performance comparison, 2D visualization, COMSOL multiphysic, MATLAB, Fortran, modelling and simulation, boundary element method, reservoir pressure

Procedia PDF Downloads 472

Authors: Ranjit Biswas

Abstract:

The existing subject Algebra is incomplete to support mathematical computations being done by scientists of all areas: Mathematics, Physics, Statistics, Chemistry, Space Science, Cosmology etc. even starting from the era of great Einstein. A huge hidden gap in the subject ‘Algebra’ is unearthed. All the scientists today, including mathematicians, physicists, chemists, statisticians, cosmologists, space scientists, and economists, even starting from the great Einstein, are lucky that they got results without facing any contradictions or without facing computational errors. Most surprising is that the results of all scientists, including Nobel Prize winners, were proved by them by doing experiments too. But in this paper, it is rigorously justified that they all are lucky. An algebraist can define an infinite number of new algebraic structures. The objective of the work in this paper is not just for the sake of defining a distinct algebraic structure, but to recognize and identify a major gap of the subject ‘Algebra’ lying hidden so far in the existing vast literature of it. The objective of this work is to fix the unearthed gap. Consequently, a different algebraic structure called ‘Region’ has been introduced, and its properties are studied.

Keywords: region, ROR, RORR, region algebra

Procedia PDF Downloads 32