Search results for: mathematical theory

Authors: Jamie A. Prowse Turner, Jamie I. D. Campbell, Valerie A. Thompson

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The objective of the current research was to use a dual-process theory framework to explain these age-related differences in reasoning. Seventy-two older (M = 80.0 years) and 72 younger (M = 24.6 years) adults were given a variety of reasoning tests (i.e., a syllogistic task, base rate task, the Cognitive Reflection Test, and a perspective manipulation), as well as independent tests of capacity (working memory, processing speed, and inhibition), thinking styles, and metacognitive ability, to account for these age-related differences. It was revealed that age-related differences were limited to problems that required Type 2 processing and were related to differences in cognitive capacity, individual difference factors, and strategy choice. Furthermore, older adults’ performance can be improved by reasoning from another’s’ perspective and cannot, at this time, be explained by metacognitive differences between young and older adults. All of these findings fit well within a dual-process theory of reasoning, which provides an integrative framework accounting for previous findings and the findings presented in the current manuscript.

Keywords: aging, dual-process theory, performance, reasoning ability

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Authors: YuPei Chang

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In recent years, moral judgement tasks have served as an increasingly popular plot mechanism in digital gameplay. As a moral agency, the player's choice judgment in digital games is to shuttle between the real world and the game world. The purpose of the research is to explore the moral difficulties brewed by the interactive mechanism of the game and the moral choice of players. In the theoretical level, this research tries to combine moral disengagement, moral foundations theory, and gameplay as an aesthetic experience. And in the methodical level, this research tries to use methods that combine text analysis, diary method, and in-depth interviews. There are three research problems that will be solved in three stages. In the first stage, this project will explore how moral dilemmas are represented in game mechanics. In the second stage, this project will analyze the appearance and conflicts of moral dilemmas in game mechanics based on the five aspects of moral foundations theory. In the third stage, this project will try to understand the players' choices when they face the choices of moral dilemmas, as well as their explanations and reflections after making the decisions.

Keywords: morality, moral disengagement, moral foundations theory, PC game, gameplay, moral dilemmas, player

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Authors: Jacob A. Braun

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

Keywords: college, condom, Herpes, mathematical modelling

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Authors: Marlone D. Severo

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

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

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Authors: Beata Jackowska-Zduniak

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

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

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Authors: Ofosuhene O. Apenteng, Noor Azina Ismail

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

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

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Authors: Korosh Khorshidi, Mohammad Khodadadi

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In this paper, exact close form solution for out of plate free flexural vibration of moderately thick rectangular nanoplates are presented based on nonlocal modified trigonometric shear deformation theory, with assumptions of the Levy's type boundary conditions, for the first time. The aim of this study is to evaluate the effect of small-scale parameters on the frequency parameters of the moderately thick rectangular nano-plates. To describe the effects of small-scale parameters on vibrations of rectangular nanoplates, the Eringen theory is used. The Levy's type boundary conditions are combination of six different boundary conditions; specifically, two opposite edges are simply supported and any of the other two edges can be simply supported, clamped or free. Governing equations of motion and boundary conditions of the plate are derived by using the Hamilton’s principle. The present analytical solution can be obtained with any required accuracy and can be used as benchmark. Numerical results are presented to illustrate the effectiveness of the proposed method compared to other methods reported in the literature. Finally, the effect of boundary conditions, aspect ratios, small scale parameter and thickness ratios on nondimensional natural frequency parameters and frequency ratios are examined and discussed in detail.

Keywords: exact solution, nonlocal modified sinusoidal shear deformation theory, out of plane vibration, moderately thick rectangular plate

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Authors: Julien Baillet

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In light of 30 years of scientific research, InCorporer Method was created in 2019 as a new approach to heal traumatic, developmental, and dissociative injuries. Following natural nervous system functions, InCorporer aims to heal, develop, and update the different defensive mammalian subsystems: fight, flight, freeze, feign death, cry for help, & energy regulator. The dimensions taken into account are: (i) Heal the traumatic injuries who are still bleeding, (ii) Develop the systems that never received the security, attention, and affection they needed. (iii) Update the parts that stayed stuck in the past, ignoring for too long that they are out of danger now. Through the Present Part and its caregiving skills, InCorporer method enables a balanced, soothed, and collaborative personality system. To be as integrative as possible, InCorporer method has been designed according to several fields of research, such as structural dissociation theory, attachment theory, and information processing theory. In this paper, the author presents how the internal caregiver is developed and trained to heal all the different parts/subsystems of our clients through mindful attention and reflex movement integration.

Keywords: PTSD, attachment, dissociation, part work

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Authors: P. W. Tsai, J. W. Chen, C. W. Chen, C. Y. Chen

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In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.

Keywords: half-circle fuzzy numbers, predictions, swarm intelligence, Lyapunov method

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Authors: Lingge Tan, Hongpeng Xu, Jieun Yang, Maarten Hornikx

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Acoustic diffusers are important components in enhancing the quality of room acoustics. This paper provides a type of modular diffuser based on the Sierpinski Triangle of the plane and combines it with fractal theory to expand the effective frequency range. In numerical calculations and full-scale model experiments, the effect of fractal design elements on normal-incidence diffusion coefficients is examined. It is demonstrated the reasonable times of iteration of modules is three, and the coverage density is 58.4% in the design frequency from 125Hz to 4kHz.

Keywords: acoustic diffuser, fractal, Sierpinski-triangle, diffusion coefficient

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Authors: Yousfi Abdelkader, Chaker Abdelkader, Bot Youcef

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This article proposes a five-level shunt active power filter for power quality improvement using a interval type-2 fuzzy logic controller (IT2 FLC). The reference compensating current is extracted using the P-Q theory. The majority of works previously reported are based on two-level inverters with a conventional Proportional integral (PI) controller, which requires rigorous mathematical modeling of the system. In this paper, a IT2 FLC controlled five-level active power filter is proposed to overcome the problem associated with PI controller. The IT2 FLC algorithm is applied for controlling the DC-side capacitor voltage as well as the harmonic currents of the five-level active power filter. The active power filter with a IT2 FLC is simulated in MATLAB Simulink environment. The simulated response shows that the proposed shunt active power filter controller has produced a sinusoidal supply current with low harmonic distortion and in phase with the source voltage.

Keywords: power quality, shunt active power filter, interval type-2 fuzzy logic controller (T2FL), multilevel inverter

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Authors: Manal Rauf

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Trained medical practitioners are produced from medical colleges serving in public and private sectors. Prime responsibility of teaching faculty is to inculcate required work ethic among the students by serving as role models for them. It is an observed fact that classroom incivility behaviours are providing a friction in achieving these targets. Present study aimed at identification of classroom incivility behaviours observed by teachers and students of public and private medical colleges as per Glasser’s Choice Theory, making a comparison and investigating the strategies being adopted by teachers of both sectors to control undesired class room behaviours. Findings revealed that a significant difference occurs between teacher and student incivility behaviours. Public sector teacher focussed on survival as a strong factor behind in civil behaviours whereas private sector teachers considered power as the precedent for incivility. Teachers of both sectors are required to use verbal as well as non-verbal immediacy to reach a healthy leaning environment.

Keywords: classroom incivility behaviour, glasser choice theory, Mehrabian immediacy theory

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Authors: Solehah Yaacob

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The study focuses on revisiting the effectiveness of Critical Thinking in human mind capability as a major faculty in human life. The tool used as a measurement of this knowledge ability consists of several processes including experience and education background. To emphasize the `Overview` concept, the researcher highlights two major aspects of philosophical approach, they are; Divine Revelation Concept and Modern Scientific Theory. The research compares between the both parties to introduce the Divine Revelation into Modern Scientific theory. An analytical and critical study of the both concepts become the methodology of the discussion.

Keywords: critical thinking, knowledge, intellectual, language

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Authors: Aydin Azizi, Aburrahman Tanira

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The main source of energy used in this modern age is fossil fuels. There is a myriad of problems that come with the use of fossil fuels, out of which the issues with the greatest impact are its scarcity and the cost it imposes on the planet. Fossil fuels are the only plausible option for many vital functions and processes; the most important of these is transportation. Thus, using this source of energy wisely and as efficiently as possible is a must. The aim of this work was to explore utilising mathematical modelling and artificial intelligence techniques to enhance fuel consumption in passenger cars by focusing on the speed at which cars are driven. An artificial neural network with an error less than 0.05 was developed to be applied practically as to predict the rate of fuel consumption in vehicles.

Keywords: mathematical modeling, neural networks, fuel consumption, fossil fuel

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Authors: Artem Sedov, Aigerim Uyzbayeva, Valeriya Tyo

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The presented article is showing results of dynamic modeling with Mathlab software of optimal automatic room climate control system for two experimental houses in Astana, one of which has circle plan and the other one has square plan. These results are showing that building geometry doesn't influence on climate system PID-controls configuring. This confirms theoretical implication that optimal automatic climate control system parameters configuring should depend on building's internal space volume, envelope heat transfer, number of people inside, supply ventilation air flow and outdoor temperature.

Keywords: climate control system, climate physics, dome-like building, mathematical modeling

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Authors: Taus Muganda

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This research explores the intricate relationship between e-procurement adoption and effective service delivery in the Uganda Coffee Industry, focusing on the processes involved, key actors, and the impact of digital transformation. The study is guided by three prominent theories, Actor-Network Theory, Resource-Based View Theory, and Institutional Theory to comprehensively explore the dynamics of e-procurement in the context of the coffee sector. The primary aim of this project is to examine the e-procurement adoption process and its role in enhancing service delivery within the Uganda Coffee Industry. The research questions guiding this inquiry are: firstly, whether e-procurement adoption and implementation contribute to achieving quality service delivery; and secondly, how e-procurement adoption can be effectively realized within the Uganda Coffee Industry. To address these questions, the study has laid out specific objectives. Firstly, it seeks to investigate the impact of e-procurement on effective service delivery, analysing how the integration of digital processes influences the overall quality of services provided in the coffee industry. Secondly, it aims to critically analyse the measures required to achieve effective delivery outcomes through the adoption and implementation of e-procurement, assessing the strategies that can maximize the benefits of digital transformation. Furthermore, the research endeavours to identify and examine the key actor’s instrumental in achieving effective service delivery within the Uganda Coffee Industry. By utilizing Actor-Network Theory, the study will elucidate the network of relationships and collaborations among actors involved in the e-procurement process. The research contributes to addressing a critical gap in the sector. Despite coffee being the leading export crop in Uganda, constituting 16% of total exports, there is a recognized need for digital transformation, specifically in the realm of e-procurement, to enhance the productivity of producers and contribute to the economic growth of the country. The study aims to provide insights into transforming the Uganda Coffee Industry by focusing on improving the e-procurement services delivered to actors in the coffee sector. The three forms of e-procurement investigated in this research—E-Sourcing, E-Payment, and E-Invoicing—serve as focal points in understanding the multifaceted dimensions of digital integration within the Uganda Coffee Industry. This research endeavours to offer practical recommendations for policymakers, industry stakeholders, and the UCDA to strategically leverage e-procurement for the benefit of the entire coffee value chain.

Keywords: e-procurement, effective service delivery, actors, actor-network theory, resource-based view theory, institutional theory, e-invocing, e-payment, e-sourcing

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Authors: Jie Xu, Zengshan Tian, Ze Li

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Previous indoor ranging or localization systems achieving high accuracy time of flight (ToF) estimation relied on two key points. One is to do strict time and frequency synchronization between the transmitter and receiver to eliminate equipment asynchronous errors such as carrier frequency offset (CFO), but this is difficult to achieve in a practical communication system. The other one is to extend the total bandwidth of the communication because the accuracy of ToF estimation is proportional to the bandwidth, and the larger the total bandwidth, the higher the accuracy of ToF estimation obtained. For example, ultra-wideband (UWB) technology is implemented based on this theory, but high precision ToF estimation is difficult to achieve in common WiFi or Bluetooth systems with lower bandwidth compared to UWB. Therefore, it is meaningful to study how to achieve high-precision ranging with lower bandwidth when the transmitter and receiver are asynchronous. To tackle the above problems, we propose a two-way channel error elimination theory and a frequency hopping-based carrier phase ranging algorithm to achieve high accuracy ranging under asynchronous conditions. The two-way channel error elimination theory uses the symmetry property of the two-way channel to solve the asynchronous phase error caused by the asynchronous transmitter and receiver, and we also study the effect of the two-way channel generation time difference on the phase according to the characteristics of different hardware devices. The frequency hopping-based carrier phase ranging algorithm uses frequency hopping to extend the equivalent bandwidth and incorporates a carrier phase ranging algorithm with multipath resolution to achieve a ranging accuracy comparable to that of UWB at 400 MHz bandwidth in the typical 80 MHz bandwidth of commercial WiFi. Finally, to verify the validity of the algorithm, we implement this theory using a software radio platform, and the actual experimental results show that the method proposed in this paper has a median ranging error of 5.4 cm in the 5 m range, 7 cm in the 10 m range, and 10.8 cm in the 20 m range for a total bandwidth of 80 MHz.

Keywords: frequency hopping, phase error elimination, carrier phase, ranging

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Authors: M. Rodionov, Z. Dedovets

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This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.

Keywords: mathematics, motivation, secondary school, student, practical problem

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Authors: Sunil Dutta

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Synchronization is defined as ‘the sequencing and re-sequencing of all relative and absolute activities in time and space and continuous alignment of those actions with purposeful objective in a complex and dynamic atmosphere. In a complex and dynamic production / maintenance setup, no single group can work in isolation for long. In addition, many activities in projects take place simultaneously at the same time. Work of every section / group is interwoven with work of others. The various activities / interactions which take place in production / overhaul workshops are interlinked because of physical requirements (information, material, workforces, equipment, and space) and dependencies. The activity sequencing is determined by physical dependencies of various department / sections / units (e.g., inventory availability must be ensured before stripping and disassembling of equipment), whereas resource dependencies do not. Theory of constraint facilitates identification, analyses and exploitation of the constraint in methodical manner. These constraints (equipment, manpower, policies etc.) prevent the department / sections / units from getting optimum exploitation of available resources. The significance of theory of constraints for achieving synchronization at overhaul workshop is illustrated in this paper.

Keywords: synchronization, overhaul, throughput, obsolescence, uncertainty

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Authors: Sergey M. Karabanov, Dmitry V. Suvorov, Dmitry Yu. Tarabrin

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The operating principle of magnetically controlled microelectromechanical system (MEMS) switches is based on controlling the beam movement under the influence of a magnetic field. Currently, there is a MEMS switch design with a flexible ferromagnetic electrode in the form of a fixed-terminal beam, with an electrode fastened on a straight or cranked anchor. The basic performance characteristics of magnetically controlled MEMS switches (service life, sensitivity, contact resistance, fast response) are largely determined by the flexible electrode design. To ensure the stable and controlled motion of the flexible electrode, it is necessary to provide the optimal design of a flexible electrode.

Keywords: flexible electrode, magnetically controlled MEMS, mathematical modeling, mechanical stress

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Authors: Beaudoin Marie-Joelle, Poirier Nathalie

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Introduction: Children with autism spectrum disorder (ASD) tend to lack socio-emotional skills (e.g., emotional regulation and theory of mind). Eisenberg’s theoretical model on emotion-related socialization behaviors suggests that mothers of children with ASD could play a central role in fostering the acquisition of socio-emotional skills by engaging in frequent educational conversations about emotions. Although, mothers’ perceptions of their own emotional skills and their child’s personality traits and social deficits could mitigate the benefit of their educative role. Objective: Our study aims to explore the association between mother-child conversations about emotions and the socio-emotional skills of their children when accounting for the moderating role of the mothers’ perceptions. Forty-nine mothers completed five questionnaires about emotionally related conversations, self-openness to emotions, and perceptions of personality and socio-emotional skills of their children with ASD. Results: Regression analyses showed that frequent mother-child conversations about emotions predicted better emotional regulation and theory of mind skills in children with ASD (p < 0.01). The children’s theory of mind was moderated by mothers’ perceptions of their own emotional openness (p < 0.05) and their perceptions of their children’s openness to experience (p < 0.01) and conscientiousness (p < 0.05). Conclusion: Mothers likely play an important role in the socio-emotional education of children with ASD. Further, mothers may be most helpful when they perceive that their interventions improve their child’s behaviors. Our findings corroborate those of the Eisenberg model, which claims that mother-child conversations about emotions predict socio-emotional development skills in children with ASD. Our results also help clarify the moderating role of mothers’ perceptions, which could mitigate their willingness to engage in educational conversations about emotions with their children. Therefore, in special needs' children education, school professionals could collaborate with mothers to increase the frequency of emotion-related conversations in ASD's students with emotion dysregulation or theory of mind problems.

Keywords: autism, parental socialization of emotion, emotional regulation, theory of mind

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Authors: Kwan U. Kim, Jin Sim, Ryong Jin Jang, Sung Duk Kim

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108 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not correctly solve one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition to it, they did not treat the astronomical and physical phenomena in a physical way based on the correct physical laws obtained from the solution of the geodesic equations in Schwarzschild metric. Therefore, some former scholars mentioned that Einstein’s theoretical basis of the general theory of relativity was obscure and incorrect, but they have not given a correct physical solution to the problems. Furthermore, since the general theory of relativity has not given a quantitative solution to obscure and incorrect problems, the generalization of gravitational theory has not been successfully completed yet, although the former scholars thought of it and tried to do it. In order to solve the problems it is necessary to explore the obscure and incorrect problems in general theory of relativity based on the physical laws and to find out the methodology of solving the problems. Therefore, first of all, as the first step for achieving the purpose, the right solution of the geodesic equation in Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results have been presented, the obscure and incorrect problems have been shown, and an analysis of them has been made based on the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild, Poincaré

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Authors: Michael Lousis

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The systematic identification of the most conspicuous and significant errors made by learners during three-years of testing of their progress in learning Arithmetic throughout the development of the Kassel Project in England and Greece was accomplished. How much retentive these errors were over three-years in the officially provided school instruction of Arithmetic in these countries has also been shown. The learners’ errors in Arithmetic stemmed from a sample, which was comprised of two hundred (200) English students and one hundred and fifty (150) Greek students. The sample was purposefully selected according to the students’ participation in each testing session in the development of the three-year project, in both domains simultaneously in Arithmetic and Algebra. Specific teaching practices have been invented and are presented in this study for subverting these learners’ errors, which were found out to be retentive to the level of the nationally provided mathematical education of each country. The invention and the development of these proposed teaching practices were founded on the rationality of the theoretical accounts concerning the explanation, prediction and control of the errors, on the conceptual metaphor and on an analysis, which tried to identify the required cognitive components and skills of the specific tasks, in terms of Psychology and Cognitive Science as applied to information-processing. The aim of the implementation of these instructional practices is not only the subversion of these errors but the achievement of the mathematical competence, as this was defined to be constituted of three elements: appropriate representations - appropriate meaning - appropriately developed schemata. However, praxis is of paramount importance, because there is no independent of science ‘real-truth’ and because praxis serves as quality control when it takes the form of a cognitive method.

Keywords: arithmetic, cognitive science, cognitive psychology, information-processing paradigm, Kassel project, level of the nationally provided mathematical education, praxis, remedial mathematical teaching practices, retentiveness of errors

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Authors: Assem M. F. Sallam, Ah. El-S. Makled

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This paper presents a study on the trajectory of a two stage launch vehicle. The study includes dynamic responses of motion parameters as well as the variation of angles affecting the orientation of the launch vehicle (LV). LV dynamic characteristics including state vector variation with corresponding altitude and velocity for the different LV stages separation, as well as the angle of attack and flight path angles are also discussed. A flight trajectory study for the drop zone of first stage and the jettisoning of fairing are introduced in the mathematical modeling to study their effect. To increase the accuracy of the LV model, atmospheric model is used taking into consideration geographical location and the values of solar flux related to the date and time of launch, accurate atmospheric model leads to enhancement of the calculation of Mach number, which affects the drag force over the LV. The mathematical model is implemented on MATLAB based software (Simulink). The real available experimental data are compared with results obtained from the theoretical computation model. The comparison shows good agreement, which proves the validity of the developed simulation model; the maximum error noticed was generally less than 10%, which is a result that can lead to future works and enhancement to decrease this level of error.

Keywords: launch vehicle modeling, launch vehicle trajectory, mathematical modeling, Matlab- Simulink

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Authors: Joon-Hoon Park

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In this paper the rationalized Haar transform is applied for distributed parameter system identification and estimation. A distributed parameter system is a dynamical and mathematical model described by a partial differential equation. And system identification concerns the problem of determining mathematical models from observed data. The Haar function has some disadvantages of calculation because it contains irrational numbers, for these reasons the rationalized Haar function that has only rational numbers. The algorithm adopted in this paper is based on the transform and operational matrix of the rationalized Haar function. This approach provides more convenient and efficient computational results.

Keywords: distributed parameter system, rationalized Haar transform, operational matrix, system identification

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Authors: V. Sankaranarayanan, V. Amrita Sundari, Sunit P. Gopal

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This paper presents the design and implementation of a nonlinear controller for the point to point control of a mobile inverted pendulum (MIP). The controller is designed based on the kinematic model of the MIP to stabilize all the four coordinates. The stability of the closed-loop system is proved using Lyapunov stability theory. The proposed controller is validated through numerical simulations and also implemented in a laboratory prototype. The results are presented to evaluate the performance of the proposed closed loop system.

Keywords: mobile inverted pendulum, switched control, nonlinear systems, lyapunov stability

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Authors: Qiuyu Chen, Bin Long, Junxi Yang

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Located in the southwest of the "roof of the world", Tibet is the origin center of Tibetan Culture.Lhasa, Shigatse and Gyantse are three famous historical and cultural cities in Tibet. They have always been prominent political, economic and cultural cities, and have accumulated the unique aesthetic orientation and value consciousness of Tibet's urban construction. "Archetype" usually refers to the theoretical origin of things, which is the collective unconscious precipitation. The archetype theory fundamentally explores the dialectical relationship between image expression, original form and behavior mode. By abstracting and describing typical phenomena or imagery of the archetype object can observe the essence of objects, explore ways in which object phenomena arise. Applying archetype theory to the field of urban planning helps to gain insight, evaluation, and restructuring of the complex and ever-changing internal structural units of cities. According to existing field investigations, it has been found that Dzong, Temple, Linka and traditional residential systems are important structural units that constitute the urban space of Lhasa, Shigatse and Gyantse. This article applies the thinking method of archetype theory, starting from the imagery expression of urban spatial pattern, using technologies such as ArcGIS, Depthmap, and Computer Vision to descriptively identify the spatial representation and plane relationship of three cities through remote sensing images and historical maps. Based on historical records, the spatial characteristics of cities in different historical periods are interpreted in a hierarchical manner, attempting to clarify the origin of the formation and evolution of urban pattern imagery from the perspectives of geopolitical environment, social structure, religious theory, etc, and expose the growth laws and key driving forces of cities. The research results can provide technical and material support for important behaviors such as urban restoration, spatial intervention, and promoting transformation in the region.

Keywords: archetype theory, urban spatial imagery, original form and pattern, behavioral driving force, Tibet

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Authors: Ana Barbir, S. Ivelic Bradanovic, D. Pecaric, J. Pecaric

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We proved a converse to Sherman's inequality. Using the concept of f-divergence we obtained some inequalities for the well-known entropies, such as Shannon entropies that have many applications in many applied sciences, for example, in information theory, biology and economics Zipf-Mandelbrot law gave improvement in account for the low-rankwords in corpus. Applications of Zipf-Mandelbrot law can be found in linguistics, information sciences and also mostly applicable in ecological eld studies. We also introduced an entropy by applying the Zipf-Mandelbrot law and derived some related inequalities.

Keywords: f-divergence, majorization inequality, Sherman inequality, Zipf-Mandelbrot entropy

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Authors: Zhanna Dedovets

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Fostering a mathematical style of thinking is crucial for cultivating intellectual personalities capable of thriving in modern society. Intuitive thinking stands as a cornerstone among the components of mathematical cognition, playing a pivotal role in grasping mathematical truths across various disciplines. This article delves into the exploration of leveraging search activities rooted in students' intuitive thinking, particularly when tackling geometric problems. Emphasizing both student engagement with the task and their active involvement in the search process, the study underscores the importance of heuristic procedures and the freedom for students to chart their own problem-solving paths. Spanning several years (2019-2023) at the Physics and Mathematics Lyceum of Dushanbe, the research engaged 17 teachers and 78 high school students. After assessing the initial levels of intuitive thinking in both control and experimental groups, the experimental group underwent training following the authors' methodology. Subsequent analysis revealed a significant advancement in thinking levels among the experimental group students. The methodological approaches and teaching materials developed through this process offer valuable resources for mathematics educators seeking to enhance their students' learning experiences effectively.

Keywords: teaching of mathematics, intuitive thinking, heuristic procedures, geometric problem, students.

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Authors: Benselama Khadidja, El Meiche Noureddine

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This paper presents the effect of hybridization material on the variation of non-dimensional critical buckling load with different cross-ply laminates plate resting on elastic foundations of Winkler and Pasternak types subjected to combine uniaxial and biaxial loading by using two variable refined plate theories. Governing equations are derived from the Principle of Virtual Displacement; the formulation is based on a new function of shear deformation theory taking into account transverse shear deformation effects vary parabolically across the thickness satisfying shear stress-free surface conditions. These equations are solved analytically using the Navier solution of a simply supported. The influence of the various parameters geometric and material, the thickness ratio, and the number of layers symmetric and antisymmetric hybrid laminates material has been investigated to find the critical buckling loads. The numerical results obtained through the present study with several examples are presented to verify and compared with other models with the ones available in the literature.

Keywords: buckling, hybrid cross-ply laminates, Winkler and Pasternak, elastic foundation, two variables plate theory

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