Search results for: mathematical beliefs

Authors: Ivan Baravy

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Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: Mitat Uysal, Aynur Uysal

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Artificial Intelligence (AI) is fundamentally driven by mathematics, with many of its core algorithms rooted in mathematical principles such as linear algebra, probability theory, calculus, and optimization techniques. This paper explores the deep connection between AI and mathematics, highlighting the role of mathematical concepts in key AI techniques like machine learning, neural networks, and optimization. To demonstrate this connection, a case study involving the implementation of a neural network using Python is presented. This practical example illustrates the essential role that mathematics plays in training a model and solving real-world problems.

Keywords: AI, mathematics, machine learning, optimization techniques, image processing

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Authors: Rasikh Tariq, Fatima Z. Benarab

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Evaporative coolers has a minimum potential to reach the wet-bulb temperature of intake air which is not enough to handle a large cooling load; therefore, it is not a feasible option to overcome cooling requirement of a building. The invention of Maisotsenko (M) cycle has led evaporative cooling technology to reach the sub-wet-bulb temperature of the intake air; therefore, it brings an innovation in evaporative cooling techniques. In this work, we developed a mathematical model of the Maisotsenko based air cooler by applying energy and mass balance laws on different air channels. The governing ordinary differential equations are discretized and simulated on MATLAB. The temperature and the humidity plots are shown in the simulation results. A parametric study is conducted by varying working air inlet conditions (temperature and humidity), inlet air velocity, geometric parameters and water temperature. The influence of these aforementioned parameters on the cooling effectiveness of the HMX is reported.  Results have shown that the effectiveness of the M-Cycle is increased by increasing the ambient temperature and decreasing absolute humidity. An air velocity of 0.5 m/sec and a channel height of 6-8mm is recommended.

Keywords: HMX, maisotsenko cycle, mathematical modeling, numerical simulation, parametric study

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Authors: Liliana M. Marinelli, Cristina T. Varanese

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

Keywords: axioms, classical physics, physical concepts, relativity

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

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

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

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Authors: Waleed Omri

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With the growth of the small business sector in emerging markets, developing a better understanding of what drives 'day-to-day' entrepreneurial activities has become an important issue for academicians and practitioners. Innovation, as an entrepreneurial behavior, revolves around individuals who creatively engage in new organizational efforts. In a similar vein, the innovation behaviors and processes at the organizational member level are central to any corporate entrepreneurship strategy. Despite the broadly acknowledged importance of entrepreneurship and innovation at the individual level in the establishment of successful ventures, the literature lacks evidence on how entrepreneurs can effectively harness their skills and knowledge in the workplace. The existing literature illustrates that religion can impact the day-to-day work behavior of entrepreneurs, managers, and employees. Religious beliefs and practices could affect daily entrepreneurial activities by fostering mental abilities and traits such as creativity, intelligence, and self-efficacy. In the present study, we define religious capital as a set of personal and intangible resources, skills, and competencies that emanate from an individual’s religious values, beliefs, practices, and experiences and may be used to increase the quality of economic activities. Religious beliefs and practices give individuals a religious satisfaction, which can lead them to perform better in the workplace. In addition, religious ethics and practices have been linked to various positive employee outcomes in terms of organizational change, job satisfaction, and entrepreneurial intensity. As investigations of their consequences beyond direct task performance are still scarce, we explore if religious capital plays a role in entrepreneurs’ innovative behavior. In sum, this study explores the determinants of individual entrepreneurial behavior by investigating the relationship between religious capital and entrepreneurs’ innovative behavior in the context of small businesses. To further explain and clarify the religious capital-innovative behavior link, the present study proposes a model to examine the mediating role of entrepreneurial creativity. We use both Islamic work ethics (IWE) and Islamic religious practices (IRP) to measure Islamic religious capital. We use structural equation modeling with a robust maximum likelihood estimation to analyze data gathered from 289 Tunisian small businesses and to explore the relationships among the above-described variables. In line with the theory of planned behavior, only religious work ethics are found to increase the innovative behavior of small businesses’ owner-managers. Our findings also clearly demonstrate that the connection between religious capital-related variables and innovative behavior is better understood if the influence of entrepreneurial creativity, as a mediating variable of the aforementioned relationship, is taken into account. By incorporating both religious capital and entrepreneurial creativity into the innovative behavior analysis, this study provides several important practical implications for promoting innovation process in small businesses.

Keywords: entrepreneurial behavior, small business, religion, creativity

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

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

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

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Authors: Divya Vats, Sanjay Mahajani

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

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

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Authors: Muleya Nqobile, Winston Garira

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

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

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Authors: Fahad Alsharari, Mohd Salmi Md. Noorani

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

Keywords: entropy, Motzkin shift, mathematical model, theory

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Authors: Nina Philipova

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

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

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

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

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

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Authors: Morteza Khorrami

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

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

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Authors: Evelyn Bilias-Lolis, Emily Louise Winter

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Schools have a responsibility to implement school-wide frameworks that actively prevent, detect, and support all aspects of child development and learning. Such efforts can range from individual or classroom-level supports to school-wide primary prevention practices for the school’s infrastructure or climate. This study assessed the perceptions of educators across a variety of disciplines in Connecticut (i.e., elementary and secondary education, special education, school psychology, and school social work) on the perceived impact of their beliefs, language, and behavior about food and body consciousness on student self-image and school climate. Participants (N=50) completed a short electronic questionnaire measuring perceptions of how their behavior can influence their students’ opinions about themselves, their emerging self-image, and the overall climate of the school community. Secondly, the beliefs that were directly assessed in the first portion of the survey were further measured through the use of applied social vignettes involving students directly or as bystanders. Preliminary findings are intriguing. When asked directly, 100% of the respondents reported that what they say to students directly could influence student opinions about themselves and 98% of participants further agreed that their behavior both to and in front of students could impact a student’s developing self-image. Likewise, 82% of the sample agreed that their personal language and behavior affect the overall climate of a school building. However, when the above beliefs were assessed via applied social vignettes depicting routine social exchanges, results were significantly more widespread (i.e., results were evenly dispersed among levels of agreement and disagreement across participants in all areas). These preliminary findings offer humble but critical implications for informing integrated school wellness frameworks that aim to create body-sensitive school communities. Research indicates that perceptions about body image, attitudes about eating, and the onset of disordered eating practices surface in school-aged years. Schools provide a natural setting for instilling foundations for child wellness as a natural extension of existing school climate reform efforts. These measures do not always need to be expansive or extreme. Rather, educators have a ripe opportunity to become champions for health and wellness through increased self-awareness and subtle shifts in language and behavior. Future psychological research needs to continue to explore this line of inquiry using larger and more varied samples of educators in order to identify needs in teacher training and development that can yield positive and preventative health outcomes for children.

Keywords: body-sensitive schools, integrated school health, school climate reform, teacher awareness

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Authors: Mohammed Darwish

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

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

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Authors: Ganiyat Soliu, Glen Bright, Chiemela Onunka

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

Keywords: performance optimization, productivity, queuing theory, robotics

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Authors: Faiqa Jalal

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The purpose of the following research paper is to discuss the differentiating meanings of culture and how popular culture has maintained a great impact on intercultural and international behavior. The following discussion leads to the notion of communicating cultural impact on behavior through advertising and sub-cultural theory in advertising. Although towards the end of the research, the complexities that develop through the above discussion, lead to the solution that ‘advertising gives meaning to the otherwise meaningless and identical objects through linking them to our basic needs’. In today’s fast paced digital world, it is difficult to define culture, literally, since its meaning tends to shift through series of different perceptions such as ‘how’ and ‘why’ it should be used. This notion can be taken towards another notion of popular culture. It is dependent on ‘attitudes, ideas, images, perspectives and other phenomena within the mainstream of a given culture’. Since popular culture is influenced by mass media, it has a way of influencing an individual’s attitude towards certain topics. For example, tattoos are a form of human decorations, that have historic significance, and a huge spectrum of meanings. Advertising is one aspect of marketing that has evolved from the time when it was ‘production oriented’, up till the time it started using different mediums to make its impact more effective. However, this impact has confused us between our needs and desires. The focus in this paper is ‘we consume to acquire a sense of social identity and status, not just for the sake of consumption’. Every culture owns different expressions, which are then used by advertisers to create its impact on the behavior of people sub-culturally and globally, as culture grows through social interaction. Advertisers furthermore play a smart role in highlighting quality of life ranging from ‘survival to well-being’. Hence, this research paper concludes by highlighting that culture is considered as a ‘basic root’ of any community that also provides solution to certain problems; however, advertisers play their part in manipulating society’s literacy and beliefs by rationalizing how relevant certain products/brands are to their beliefs.

Keywords: mass media, popular culture, production oriented, sub-culture

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Authors: Khashayar Kazemzadeh, Mohammad Hanif Dasoomi

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

Keywords: urban highway, accident, tunnel, mathematical model

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Authors: Kairat Kurakbayev, Dina Gungor, Adil Ashirbekov, Assel Kambatyrova

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Kazakhstan, a post-Soviet economy located in the Central Asia, is making great efforts to internationalize its national system of education. The country is very ambitious in making the national economy internationally competitive and education has become one of the main pillars of the nation’s strategic development plan for 2030. This paper discusses the role of professional teacher development in upgrading the secondary education curriculum with the introduction of English as a medium of instruction (EMI) in grades 10-11 grades. Having Kazakh as the state language and Russian as the official language, English bears a status of foreign language in the country. The development of trilingual education is very high on the agenda of the Ministry of Education and Science. It is planned that by 2019 STEM-related subjects – Biology, Chemistry, Computing and Physics – will be taught in EMI. Introducing English-medium education appears to be a very drastic reform and the teaching cadre is the key driver here. At the same time, after the collapse of the Soviet Union, the teaching profession is still struggling to become attractive in the eyes of the local youth. Moreover, the quality of Kazakhstan’s secondary education is put in question by OECD national review reports. The paper presents a case study of the nation-wide professional development programme arranged for 5 010 school teachers so that they could be able to teach their content subjects in English starting from 2019 onwards. The study is based on the mixed methods research involving the data derived from the surveys and semi-structured interviews held with the programme participants, i.e. school teachers. The findings of the study imply the significance of the school teachers’ attitudes towards the top-down reform of trilingual education. The qualitative research data reveal the teachers’ beliefs about advantages and disadvantages of having their content subjects (e.g. Biology or Chemistry) taught in EMI. The study highlights teachers’ concerns about their professional readiness to implement the top-down reform of English-medium education and discusses possible risks of academic underperforming on the part of students whose English language proficiency is not advanced. This paper argues that for the effective implementation of the English-medium education in secondary schools, the state should adopt a comprehensive approach to upgrading the national academic system where teachers’ attitudes and beliefs play the key role in making the trilingual education policy effective. The study presents lessons for other national academic systems considering to transfer its secondary education to English as a medium of instruction.

Keywords: teacher education, teachers' beliefs, trilingual education, case study

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Authors: Ogunrinde Roseline Bosede, Ogunrinde Rowland Rotimi

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

Keywords: computer, impacts, mathematics, modern society

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

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

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

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Authors: Chakib Jerry, Mounir Jerry

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

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

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Authors: Amira Abdelrasoul, Huu Doan, Ali Lohi

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An efficient and well-planned ultrafiltration process is becoming a necessity for monetary returns in the industrial settings. The aim of the present study was to develop a mathematical model for an accurate prediction of ultrafiltration membrane fouling of latex effluent applied to homogeneous and heterogeneous membranes with uniform and non-uniform pore sizes, respectively. The models were also developed for an accurate prediction of power consumption that can handle the large-scale purposes. The model incorporated the fouling attachments as well as chemical and physical factors in membrane fouling for accurate prediction and scale-up application. Both Polycarbonate and Polysulfone flat membranes, with pore sizes of 0.05 µm and a molecular weight cut-off of 60,000, respectively, were used under a constant feed flow rate and a cross-flow mode in ultrafiltration of the simulated paint effluent. Furthermore, hydrophilic ultrafilic and hydrophobic PVDF membranes with MWCO of 100,000 were used to test the reliability of the models. Monodisperse particles of 50 nm and 100 nm in diameter, and a latex effluent with a wide range of particle size distributions were utilized to validate the models. The aggregation and the sphericity of the particles indicated a significant effect on membrane fouling.

Keywords: membrane fouling, mathematical modeling, power consumption, attachments, ultrafiltration

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Authors: M. Khoshab, M. J. Sedigh

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Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.

Keywords: dynamic system, lag on supply demand, market stability, supply demand model

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Authors: Gülcan Taşkıran, Ayla Bayık Temel

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Background: Florence Nightingale, the modern founder of the nursing, is most famous for her role as a nurse. But not so much known about her contributions as a mathematician and statistician. Aim: In this conceptual article it is aimed to examine Florence Nightingale's statistics education, how she used her passion for statistics and applied statistical data in nursing care and her scientific contributions to statistical science. Design: Literature review method was used in the study. The databases of Istanbul University Library Search Engine, Turkish Medical Directory, Thesis Scanning Center of Higher Education Council, PubMed, Google Scholar, EBSCO Host, Web of Science were scanned to reach the studies. The keywords 'statistics' and 'Florence Nightingale' have been used in Turkish and English while being screened. As a result of the screening, totally 41 studies were examined from the national and international literature. Results: Florence Nightingale has interested in mathematics and statistics at her early ages and has received various training in these subjects. Lessons learned by Nightingale in a cultured family environment, her talent in mathematics and numbers, and her religious beliefs played a crucial role in the direction of the statistics. She was influenced by Quetelet's ideas in the formation of the statistical philosophy and received support from William Farr in her statistical studies. During the Crimean War, she applied statistical knowledge to nursing care, developed many statistical methods and graphics, so that she made revolutionary reforms in the health field. Conclusions: Nightingale's interest in statistics, her broad vision, the statistical ideas fused with religious beliefs, the innovative graphics she has developed and the extraordinary statistical projects that she carried out has been influential on the basis of her professional achievements. Florence Nightingale has also become a model for women in statistics. Today, using and teaching of statistics and research in nursing care practices and education programs continues with the light she gave.

Keywords: Crimean war, Florence Nightingale, nursing, statistics

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Authors: Bi̇rsen Tutunis, Zuhal Aydin

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Guided digital learning has attracted many researchers as it leads to autonomous learning.The developments in Guided digital learning have led to changes in teaching and learning in English Language Teaching classes (Jeong-Bae, 2014). This study reports on tasks designed under the principles of learner autonomy in an online learning platform ‘’Webquest’’ with the purpose of teaching English to Turkish tertiary level students at a foundation university in Istanbul. Guided digital learning blog project contents were organized according to work-cycles phases (planning and negotiation phase, decision-making phase, project phase and evaluation phase) which are compatible with the principles of autonomous learning (Legenhausen,2003). The aim of the study was to implement the class blog project to find out its impact on students’ behaviours and beliefs towards autonomous learning. The mixed method research approach was taken. 24 tertiary level students participated in the study on voluntary basis. Data analysis was performed with Statistical Package for the Social Sciences. According to the results, students' attitudes towards digital learning did not differ before and after the training application. The learning styles of the students and their knowledge on digital learning scores differed. It has been observed that the students' learning styles and their digital learning scores increased after the training application. Autonomous beliefs, autonomous behaviors, group cohesion and group norms differed before and after the training application. Students' motivation level, strategies for learning English, perceptions of responsibility and out-of-class activity scores differed before and after the training application. It was seen that work-cycles in online classes create student centered learning that fosters autonomy. This paper will display the work cycles in detail and the researchers will give examples of in and beyond class activities and blog projects.

Keywords: guided digital learning, work cycles, english language teaching, autonomous learning

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Authors: Jitendra Singh, Vivek Kumar

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In this paper, a susceptible infective susceptible mathematical model is proposed and analyzed where the migration of human population is given by migration function. It is assumed that the disease is transmitted by direct contact of susceptible and infective populations with constant contact rate. The equilibria and their stability are studied by using the stability theory of ordinary differential equations and computer simulation. The model analysis shows that the spread of infectious disease increases when human population immigration increases in the habitat but it decreases if emigration increases.

Keywords: SIS (Susceptible Infective Susceptible) model, migration function, susceptible, stability

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Authors: Amanbek Jainakov, Abdikerim Kurbanaliev

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The work presents the results of mathematical modeling of large-scale flows in areas with a complex topographic relief. The Reynolds-averaged Navier—Stokes equations constitute the basis of the three-dimensional unsteady modeling. The well-known Volume of Fluid method implemented in the solver interFoam of the open package OpenFOAM 2.3 is used to track the free-boundary location. The mathematical model adequacy is checked by comparing with experimental data. The efficiency of the applied technology is illustrated by the example of modeling the breakthrough of the dams of the Andijan (Uzbekistan) and Papan (near the Osh town, Kyrgyzstan) reservoir.

Keywords: three-dimensional modeling, free boundary, the volume-of-fluid method, dam break, flood, OpenFOAM

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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

Abstract:

This report is about the Photomath app, which is an AI application that uses image recognition technology, specifically optical character recognition (OCR) algorithms. The (OCR) algorithm translates the images into a mathematical equation, and the app automatically provides a step-by-step solution. The application supports decimals, basic arithmetic, fractions, linear equations, and multiple functions such as logarithms. Testing was conducted to examine the usage of this app, and results were collected by surveying ten participants. Later, the results were analyzed. This paper seeks to answer the question: To what level the artificial intelligence features are accurate and the speed of process in this app. It is hoped this study will inform about the efficiency of AI in Photomath to the users.

Keywords: photomath, image recognition, app, OCR, artificial intelligence, mathematical equations.

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