Search results for: introductory mathematics

Authors: Ayaz Ahmad

Abstract:

TOPIC: A study of the formation ,existness and stability of localised pulses in pde Ayaz Ahmad ,NITP, Abstract:In this paper we try to govern the evolution deterministic variable over space and time .We analysis the behaviour of the model which allows us to predict and understand the possible behaviour of the physical system .Bifurcation theory provides a basis to systematically investigate the models for invariant sets .Exploring the behaviour of PDE using bifurcation theory which provides many challenges both numerically and analytically. We use the derivation of a non linear partial differential equation which may be written in this form ∂u/∂t+c ∂u/∂x+∈(∂^3 u)/(∂x^3 )+¥u ∂u/∂x=0 We show that the temperature increased convection cells forms. Through our work we look for localised solution which are characterised by sudden burst of aeroidic spatio-temporal evolution. Key word: Gaussian pulses, Aeriodic ,spatio-temporal evolution ,convection cells, nonlinearoptics, Dr Ayaz ahmad Assistant Professor Department of Mathematics National institute of technology Patna ,Bihar,,India 800005 [email protected] +91994907553

Keywords: Gaussian pulses, aeriodic, spatio-temporal evolution, convection cells, nonlinear optics

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Authors: Samir Sarfraj Terdalkar

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India needs to step into affordable higher education with more focus on skill development and employability. The general scenario of higher education in India revolves around two major branches of higher education ie., Engineering and Medical Sciences. These two branches still cannot be considered as affordable. Hence, skill development of each and every student beginning from the school education should emphasize on learning skills with special focus on physics and mathematics. In India, the Central Government initiated a survey based process of all higher Educational Institutes/ Universities and colleges in India. This survey/ process was – All India Survey On Higher Education (AISHE). The focus of this process was understand and Though the increase is significant, it is necessary to propagate skill and vocational education which would add to the employability factor. Similarly, there has been a significant increase in number of higher education institutes, there is need to rethink on the type of education/ curriculum offered by these institutions. In this regard, vocational education has helped to build skill sets to certain extent. There is need to bring in this vocational educational in main stream education which could be complementary for undergraduate / post graduate education. The paper focuses on different policies to bring in vocational/ skill education.

Keywords: higher education, skill, vocational, India

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Authors: Muhammad Luqman, Yusuf Kurniawan

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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

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Authors: Ranjit Biswas

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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

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

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Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization

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Authors: Baghdad Said

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Differential equations of fractional order have proved to be important tools to describe many physical phenomena and have been used in diverse fields such as engineering, mathematics as well as other applied sciences. On the other hand, the theory of differential equations involving the Stieltjes derivative (SD) with respect to a non-decreasing function is a new class of differential equations and has many applications as a unified framework for dynamic equations on time scales and differential equations with impulses at fixed times. The aim of this paper is to investigate the existence, uniqueness, and generalized Ulam-Hyers-Rassias stability (UHRS) of solutions for a boundary value problem of sequential fractional differential equations (SFDE) containing (SD). This study is based on the technique of noncompactness measures (MNCs) combined with Monch-Krasnoselski fixed point theorems (FPT), and the results are proven in an appropriate Banach space under sufficient hypotheses. We also give an illustrative example. In this work, we introduced a class of (SFDE) and the results are obtained under a few hypotheses. Future directions connected to this work could focus on another problem with different types of fractional integrals and derivatives, and the (SD) will be assumed under a more general hypothesis in more general functional spaces.

Keywords: SFDE, SD, UHRS, MNCs, FPT

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Authors: Amal A. Abdel-Sattar

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The curriculum of architecture department in Prince Sultan University includes ‘Building Surveying’ course which is usually a part of civil engineering courses. As a fundamental requirement of the course, it requires a strong background in mathematics and physics, which are not usually preferred subjects to the architecture students and many of them are not giving the required and necessary attention to these courses during their preparation year before commencing their architectural study. This paper introduces the concept and the methodology of the student-centered learning approach in the course of building surveying for architects. One of the major outcomes is the improvement in the students’ involvement in the course and how this will cover and strength their analytical weak points and improve their mathematical skills. The study is conducted through three semesters with a total number of 99 students. The effectiveness of the student-centered learning approach is studied using the student survey at the end of each semester and teacher observations. This survey showed great acceptance of the students for these methods. Also, the teachers observed a great improvement in the students’ mathematical abilities and how keener they became in attending the classes which were clearly reflected on the low absence record.

Keywords: architecture, building surveying, student-centered learning, teaching and learning

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

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Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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Authors: Nicoly Coelho, Eduardo Vieira Vilas Boas, Paulo Orestes Formigoni

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Faced with the remarkable developments in the various segments of modern engineering, provided by the increasing technological development, professionals of all educational areas need to overcome the difficulties generated due to the good understanding of those who are starting their academic journey. Aiming to overcome these difficulties, this article aims at an introduction to the basic study of numerical methods applied to fluid mechanics and thermodynamics, demonstrating the modeling and simulations with its substance, and a detailed explanation of the fundamental numerical solution for the use of finite difference method, using SCILAB, a free software easily accessible as it is free and can be used for any research center or university, anywhere, both in developed and developing countries. It is known that the Computational Fluid Dynamics (CFD) is a necessary tool for engineers and professionals who study fluid mechanics, however, the teaching of this area of knowledge in undergraduate programs faced some difficulties due to software costs and the degree of difficulty of mathematical problems involved in this way the matter is treated only in postgraduate courses. This work aims to bring the use of DFC low cost in teaching Transport Phenomena for graduation analyzing a small classic case of fundamental thermodynamics with Scilab® program. The study starts from the basic theory involving the equation the partial differential equation governing heat transfer problem, implies the need for mastery of students, discretization processes that include the basic principles of series expansion Taylor responsible for generating a system capable of convergence check equations using the concepts of Sassenfeld, finally coming to be solved by Gauss-Seidel method. In this work we demonstrated processes involving both simple problems solved manually, as well as the complex problems that required computer implementation, for which we use a small algorithm with less than 200 lines in Scilab® in heat transfer study of a heated plate in rectangular shape on four sides with different temperatures on either side, producing a two-dimensional transport with colored graphic simulation. With the spread of computer technology, numerous programs have emerged requiring great researcher programming skills. Thinking that this ability to program DFC is the main problem to be overcome, both by students and by researchers, we present in this article a hint of use of programs with less complex interface, thus enabling less difficulty in producing graphical modeling and simulation for DFC with an extension of the programming area of experience for undergraduates.

Keywords: numerical methods, finite difference method, heat transfer, Scilab

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Authors: Judit Nagy

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Many scientific studies claim that financial education should start as early as possible. Children are much more capable of and willing to absorb new concepts than adults. If we introduce children to financial knowledge early, their behaviour and attitudes to this subject will change, increasing later success in this area of life. However, poor financial decisions may entail severe consequences, not only to individuals but even to the wider society. Good financial decisions and economic attitudes may contribute to economic growth and well-being. Whilst in several countries, education about financial awareness and fundamentals is available, the understanding and acquisition of complex economic knowledge and the development of children’s independent problem-solving skills are still lacking. The results suggest that teaching economic and financial knowledge through accounting and making lectures interactive by using special tools of positive education is critical to stimulating children’s interest. Eighty percent of the students in the study liked the combined and interactive lecture. Introducing this kind of knowledge to individuals is a relevant objective, even at the societal level.

Keywords: positive psychology, education innovation, primary school, gender, economics, accounting, finance, personal finance, mathematics, economic growth, well-being, sustainability

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Authors: Frederic Jumelle, Kelvin So, Didan Deng

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In this paper, we are introducing a model of artificial general intelligence (AGI), the functional neural network (FNN), for modeling human decision-making processes. The FNN is composed of multiple artificial mirror neurons (AMN) racing in the network. Each AMN has a similar structure programmed independently by the users and composed of an intention wheel, a motor core, and a sensory core racing at a specific velocity. The mathematics of the node’s formulation and the racing mechanism of multiple nodes in the network will be discussed, and the group decision process with fuzzy logic and the transformation of these conceptual methods into practical methods of simulation and in operations will be developed. Eventually, we will describe some possible future research directions in the fields of finance, education, and medicine, including the opportunity to design an intelligent learning agent with application in AGI. We believe that FNN has a promising potential to transform the way we can compute decision-making and lead to a new generation of AI chips for seamless human-machine interactions (HMI).

Keywords: neural computing, human machine interation, artificial general intelligence, decision processing

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Authors: M. Yushalify Misro, Ahmad Ramli, Jamaludin M. Ali

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Bezier curves have useful properties for path generation problem, for instance, it can generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segment smoothly to generate the path. Some of the useful properties of Bezier are curvature. In mathematics, the curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line. Another extrinsic example of curvature is a circle, where the curvature is equal to the reciprocal of its radius at any point on the circle. The smaller the radius, the higher the curvature thus the vehicle needs to bend sharply. In this study, we use Bezier curve to fit highway-like curve. We use the different approach to finding the best approximation for the curve so that it will resemble highway-like curve. We compute curvature value by analytical differentiation of the Bezier Curve. We will then compute the maximum speed for driving using the curvature information obtained. Our research works on some assumptions; first the Bezier curve estimates the real shape of the curve which can be verified visually. Even, though, the fitting process of Bezier curve does not interpolate exactly on the curve of interest, we believe that the estimation of speed is acceptable. We verified our result with the manual calculation of the curvature from the map.

Keywords: speed estimation, path constraints, reference trajectory, Bezier curve

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Authors: Kalliopi Kanaki, Michael Kalogiannakis

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Nowadays, in the digital era, the early acquisition of basic programming skills and knowledge is encouraged, as it facilitates students’ exposure to computational thinking and empowers their creativity, problem-solving skills, and cognitive development. More and more researchers and educators investigate the introduction of computational thinking in K-12 since it is expected to be a fundamental skill for everyone by the middle of the 21st century, just like reading, writing and arithmetic are at the moment. In this paper, a doctoral research in the process is presented, which investigates the infusion of computational thinking into science curriculum in early childhood education. The whole attempt aims to develop young children’s computational thinking by introducing them to the fundamental concepts of object-oriented programming in an enjoyable, yet educational framework. The backbone of the research is the digital environment PhysGramming (an abbreviation of Physical Science Programming), which provides children the opportunity to create their own digital games, turning them from passive consumers to active creators of technology. PhysGramming deploys an innovative hybrid schema of visual and text-based programming techniques, with emphasis on object-orientation. Through PhysGramming, young students are familiarized with basic object-oriented programming concepts, such as classes, objects, and attributes, while, at the same time, get a view of object-oriented programming syntax. Nevertheless, the most noteworthy feature of PhysGramming is that children create their own digital games within the context of physical science courses, in a way that provides familiarization with the basic principles of object-oriented programming and computational thinking, even though no specific reference is made to these principles. Attuned to the ethical guidelines of educational research, interventions were conducted in two classes of second grade. The interventions were designed with respect to the thematic units of the curriculum of physical science courses, as a part of the learning activities of the class. PhysGramming was integrated into the classroom, after short introductory sessions. During the interventions, 6-7 years old children worked in pairs on computers and created their own digital games (group games, matching games, and puzzles). The authors participated in these interventions as observers in order to achieve a realistic evaluation of the proposed educational framework concerning its applicability in the classroom and its educational and pedagogical perspectives. To better examine if the objectives of the research are met, the investigation was focused on six criteria; the educational value of PhysGramming, its engaging and enjoyable characteristics, its child-friendliness, its appropriateness for the purpose that is proposed, its ability to monitor the user’s progress and its individualizing features. In this paper, the functionality of PhysGramming and the philosophy of its integration in the classroom are both described in detail. Information about the implemented interventions and the results obtained is also provided. Finally, several limitations of the research conducted that deserve attention are denoted.

Keywords: computational thinking, early childhood education, object-oriented programming, physical science courses

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Authors: V. S. Klimash, Ye Min Thu

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Thyristor rectifiers, inverters grid-tied, and AC voltage regulators are widely used in industry, and on electrified transport, they have a lot in common both in the power circuit and in the control system. They have a common mathematical structure and switching processes. At the same time, the rectifier, but the inverter units and thyristor regulators of alternating voltage are considered separately both theoretically and practically. They are written about in different books as completely different devices. The aim of this work is to combine them into one class based on the unity of the equations describing electromagnetic processes, and then, to show this unity on the mathematical model and experimental setup. Based on research from mathematics to the product, a conclusion is made about the methodology for the rapid conduct of research and experimental design work, preparation for production and serial production of converters with a unified bundle. In recent years, there has been a transition from thyristor circuits and transistor in modular design. Showing the example of thyristor rectifiers and AC voltage regulators, we can conclude that there is a unity of mathematical structures and grid-tied thyristor converters.

Keywords: direct current, alternating current, rectifier, AC voltage regulator, generalized mathematical model

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Authors: Nasrin Mohammadhasani, Rosa Angela Fabio

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The attention to relevance information is the key element for learning. Otherwise, Attention Deficit Hyperactivity Disorder (ADHD) students have a fuzzy visual pattern that prevents them to attention and remember learning subject. The present study aimed to test the hypothesis that the presence of a pedagogical agent can effectively support ADHD learner's attention and learning outcomes in a multimedia learning environment. The learning environment was integrated with a pedagogical agent, named Koosha as a social peer. This study employed a pretest and posttest experimental design with control group. The statistical population was 30 boys students, age 10-11 with ADHD that randomly assigned to learn with/without an agent in well designed environment for mathematic. The results suggested that experimental and control groups show a significant difference in time when they participated and mathematics achievement. According to this research, using the pedagogical agent can enhance learning of ADHD students by gaining and guiding their attention to relevance information part on display, so it can be considered as asocial cue that provides theme cognitive supports.

Keywords: attention, computer assisted instruction, multimedia learning environment, pedagogical agent

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Authors: Aqleem Fatimah

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The purpose of study was to find out the impact of teachers’ gender on students’ score achievement. Focusing on primary level’s teachers & students, a survey research was conducted by using convenient sampling technique. All the students of grade four (1500) and fifty-six teachers (equally divided by gender) from the 50 randomly selected coeducational schools from Lahore were taken as sample. The academic performance was operationalized using a t-test on standardized achievement tests of the students in language, science mathematics and social studies. In addition, all those gender based characteristics of teachers that count a lot in classroom interactions (taking Multi-grade classes, classroom strategies, feedback strategies and evaluation method) that influence students’ achievement were also analyzed by using a questionnaire and an observation schedule. The results of the study showed better academic achievement of students (girl &boy) of female teachers comparatively to the students of male teachers. Therefore, as the female teachers’ number lacks in Pakistan, the study suggests policy makers to seek guidelines to induct more specialized and professionally competent female teachers because their induction will prove highly beneficial for the betterment of students’ score achievement.

Keywords: gender, teacher, competency, score achievement

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Authors: Abdullah Abu-Tineh, Youmen Chaaban

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This study examines the development of a professional development (PD) model for teacher growth and learning that is embedded into the school context. The School based Support Program (SBSP), designed for the Qatari context, targets the practices, knowledge and skills of both school leadership and teachers in an attempt to improve student learning outcomes. Key aspects of the model include the development of learning communities among teachers, strong leadership that supports school improvement activities, and the use of research-based PD to improve teacher practices and student achievement. This paper further presents findings from an evaluation of this PD program. Based on an adaptation of Guskey’s evaluation of PD models, 100 teachers at the participating schools were selected for classroom observations and 40 took part in in-depth interviews to examine changed classroom practices. The impact of the PD program on student learning was also examined. Teachers’ practices and their students’ achievement in English, Arabic, mathematics and science were measured at the beginning and at the end of the intervention.

Keywords: initiative, professional development, school based support Program (SBSP), school reform

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Authors: Michael Shulman, Paige North, Benedikt Ahrens, Dmitris Tsementzis

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The Univalence Principle is the statement that equivalent mathematical structures are indistinguishable. We prove a general version of this principle that applies to all set-based, categorical, and higher-categorical structures defined in a non-algebraic and space-based style, as well as models of higher-order theories such as topological spaces. In particular, we formulate a general definition of indiscernibility for objects of any such structure, and a corresponding univalence condition that generalizes Rezk’s completeness condition for Segal spaces and ensures that all equivalences of structures are levelwise equivalences. Our work builds on Makkai’s First-Order Logic with Dependent Sorts, but is expressed in Voevodsky’s Univalent Foundations (UF), extending previous work on the Structure Identity Principle and univalent categories in UF. This enables indistinguishability to be expressed simply as identification, and yields a formal theory that is interpretable in classical homotopy theory, but also in other higher topos models. It follows that Univalent Foundations is a fully equivalence-invariant foundation for higher-categorical mathematics, as intended by Voevodsky.

Keywords: category theory, higher structures, inverse category, univalence

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Authors: D. Mulligan, D. Casey

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Introductory Statement: Delegation is when a registered nurse (RN) transfers a task or activity that is normally within their scope of practice to another person (delegatee). RN delegation is common practice with unregistered staff, e.g., student nurses and health care assistants (HCAs). As the role of the HCA is increasingly embedded as a direct care and support role, especially in long-term residential care for older adults, there is RN uncertainty as to their role as a delegator. The assignment is when a task is transferred to a person that is within the role specification of the delegatee. RNs in long-term care (LTC) for older people are increasingly working in teams where there are less RNs and more HCAs providing direct care to the residents. The RN is responsible and accountable for their decision to delegate and assign tasks to HCAs. In an interpretive, multiple case studies to explore how delegation of tasks by RNs to HCAs occurred in long-term care settings in Ireland the importance of the RN understanding their scope of practice emerged. Methodology: Focus group interviews and individual interviews were undertaken as part of a multiple case study. Both cases, anonymized as Case A and Case B, were within the public health service in Ireland. The case study sites were long-term care settings for older adults located in different social care divisions, and in different geographical areas. Four focus group interviews with staff nurses and three individual interviews with CNMs were undertaken. The interactive data analysis approach was the analytical framework used, with within-case and cross-case analysis. The theoretical lens of organizational role theory, applying the role episode model (REM), was used to understand, interpret, and explain the findings. Study Findings: RNs and CNMs understood the role of the nurse regulator and the scope of practice. RNs understood that the RN was accountable for the care and support provided to residents. However, RNs and CNM2s could not describe delegation in the context of their scope of practice. In both cases, the RNs did not have a standardized process for assessing HCA competence to undertake nursing tasks or interventions. RNs did not routinely supervise HCAs. Tasks were assigned and not delegated. There were differences between the cases in relation to understanding which nursing tasks required delegation. HCAs in Case A undertook clinical vital sign assessments and documentation. HCAs in Case B did not routinely undertake these activities. Delegation and assignment were influenced by the organizational factors, e.g., model of care, absence of delegation policies, inadequate RN education on delegation, and a lack of RN and HCA role clarity. Concluding Statement: Nurse staffing levels and skill mix in long-term care settings continue to change with more HCAs providing more direct care and support. With decreasing RN staffing levels RNs will be required to delegate and assign more direct care to HCAs. There is a requirement to distinguish between RN assignment and delegation at policy, regulation, and organizational levels.

Keywords: assignment, delegation, registered nurse, scope of practice

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Authors: Saleit Ron

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The Mitar program was established to drive a shift in middle school mathematics education, emphasizing the connection of math to real-life situations, exploring mathematical modeling and literacy, and integrating social and emotional learning (SEL) components for enhanced excellence. The program envisions math coordinators as catalysts for change, equipping them to create educational materials, strengthen leadership skills, and develop SEL competencies within coordinator communities. These skills are then employed to lead transformative efforts within their respective schools. The program engaged 90 participants across six math coordinator communities during 2022-2023, involving 30-60 hours of annual learning. The process includes formative and summative evaluations through questionnaires and interviews, revealing participants' high contentment and successful integration of acquired skills into their schools. Reflections from participants highlighted the need for enhanced change leadership processes, often seeking more personalized mentoring to navigate challenges effectively.

Keywords: math coordinators, mathematical literacy, mathematical modeling, SEL competencies

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Authors: Suzanne El Takach

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The research study explored pre-service teachers’ attitudes towards 6 courses taught in 3rd till 6th semesters at the Faculty of Education, Lebanese University, during the academic year 2015-2016. They assessed science teaching courses that are essential for teacher preparation for Science at the primary and elementary level. These courses were: Action Research I and II in Teaching Science, New trends in Teaching Science, Teaching Science I and II for the elementary level and Teaching Science for Early Childhood Education. Qualitative and Quantitative Data were gathered from a) a survey questionnaire consisting of 23 closed-ended items; some were of Likert scale type, that aimed at collecting students’ opinions on courses, in terms of teaching, assessment and class interaction (N=102 respondents) and b) a second questionnaire of 10 questions was disseminated on a sample of 39 students in their last semester in science and Mathematics, in order to know more about students’ skills gained, suggestions for new courses and improvement. Students were satisfied with science teaching courses and they have admitted that they gained a good pedagogical content knowledge, such as, lesson planning, students’ misconceptions, and use of various teaching and assessment strategies.

Keywords: assessment in higher education, LMD program, pre-service teachers’ attitudes, pre-PCK skills

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Authors: Raliatu Mohammed Kashim

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The study investigated primary school teachers conceptual and procedural knowledge of rational numbers to determine how it effects on pupil’s achievement on rational number. Specifically, primary school teachers’ level of conceptual and procedural knowledge about rational number and its effects on their pupils understanding of rational number in primary school was explored. The study was carried out in Bauchi state of Nigeria, Using a multistage design. The first stage was a descriptive design. The second stage involves a pre-test post-test only quasi experiment design. The population of the study comprises of six mathematics teachers holding the Nigerian Certificate in Education (NCE) teaching primary six and their two hundred and ten pupils in intact class. Two instrument namely Conceptual and Procedural knowledge Test (CPKT) and Rational number Achievement Test (RAT) were used for data collection. Data collected was analyzed using ANCOVA and Scheffe’s Test. The result revealed a significant differences between pupils taught by teachers with high conceptual and procedural knowledge and those target by teachers with low conceptual and procedural knowledge.

Keywords: conceptual knowledge, procedural knowledge, rational numbers, multistage design

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Authors: Sophie Huck, Knut Linke

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This study will examine how IT practitioners can be motivated for IT studies and which kind of support they need during their occupational studies. Within this research project, the challenge of supporting students being engaged in business for several years arose. Here, it is especially important to successfully guide them through their studies. The problem of this group is that they finished their school education years ago. In order to gather first experiences, preliminary e-learning courses were introduced and tested with a group of users studying General Management. They had to work with these courses and have been questioned later on about their approach to the different methods. Moreover, a second group of potential students was interviewed with the help of online questionnaires to give information about their expectations regarding extra occupational studies. We also want to present best practices and cases in e-education in the subarea of mathematics and distance learning. Within these cases and practices, we use state of the art systems and technologies in e-education to find a way to increase teaching quality and the success of students. Our research indicated that the first group of enrolled students appreciated the new preliminary e-learning courses. The second group of potential students was convinced of this way of learning as a significant component of extra occupational studies. It can be concluded that this part of the project clarified the acceptance of the e-learning strategy by both groups and led to satisfactory results with the enrolled students.

Keywords: e-learning evaluation, self-learning, virtual classroom, virtual learning environments

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Authors: Lindsey D. Sams, Dean R. Gorman, Cathy D. Lirgg, Steve W. Dittmore, Jack C. Kern

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Golf is a lifetime sport that provides numerous physical and psychological benefits. The game has struggled with attrition and retention within minority groups and this has exposed the lack of a modified introduction to the game that is uniformly accessible and developmentally appropriate. Factors that have been related to sport participatory behaviors include perceived competence, enjoyment and intention. The purpose of this study was to examine self-reported perception differences in competence and enjoyment between learners using modified and traditional equipment as well as the potential effects these factors could have on intent for future participation. For this study, SNAG Golf was chosen to serve as the scaled equipment used by the modified equipment group. The participants in this study were 99 children (24 traditional equipment users/ 75 modified equipment users) located across the U.S. with ages ranging from 7 to 12 years (2nd-5th grade). Utilizing a convenience sampling method, data was obtained on a voluntary basis through surveys measuring children’s golf participation and self-perceptions concerning perceived competence, enjoyment and intention to continue participation. The scales used for perceived competence and enjoyment included Susan Harter’s Self-Perception Profile for Children (SPPC) along with the Physical Activity Enjoyment Scale (PACES). Analysis revealed no significant differences for enjoyment, perceived competence or intention between children learning with traditional golf equipment and modified golf equipment. This was true even though traditional equipment users reported significantly higher experience levels than that of modified users. Intention was regressed on the enjoyment and perceived competence variables. Congruent with current literature, enjoyment was a strong predictor of intention to continue participation, for both groups. Modified equipment users demonstrated significantly lower experience levels but reported similar levels of competence, enjoyment and intent to continue participation as reported by the more experienced, and potentially more skilled, traditional users. The ability to immediately generate these positive affects suggests the potential adoption of a more effective way to learn golf and a method that is conducive to participatory behaviors related to attrition and retention. These implications in turn, highlight an equipment candidate ideal for inception into physical education programs where new learners are introduced to various sports in safe and developmentally appropriate environments. A major goal of this study was to provide foundational research that instigates the further examination of golf’s introductory teaching methodologies, as there is a lack of its presence in current literature. Future research recommendations range from improvements in the current research design to expansive approaches related to the topic, such as progressive skill development, knowledge of the game’s tactical and strategic concepts, playing ability and teaching effectiveness when utilizing modified versus traditional equipment.

Keywords: adaptive sports, enjoyment, golf participation, modified equipment, perceived competence, SNAG golf

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Authors: Nicolae Pascu

Abstract:

Aside from being a fundamental tool in Complex analysis, Schwarz Lemma-which was finalized in its most complete form at the beginning of the last century-generated an important area of research in various fields of mathematics, which continues to advance even today. We present some properties of analytic functions in the half-plane which satisfy the conditions of the classical Schwarz Lemma (Carathéodory functions) and obtain a generalization of the well-known Aleksandrov-Sobolev Lemma for analytic functions in the half-plane (the correspondent of Schwarz-Pick Lemma from the unit disk). Using this Schwarz-type lemma, we obtain a characterization for the entire class of Carathéodory functions, which might be of independent interest. We prove two monotonicity properties for Carathéodory functions that do not depend upon their normalization at infinity (the hydrodynamic normalization). The method is based on conformal mapping arguments for analytic functions in the half-plane satisfying appropriate conditions, in the spirit of Schwarz lemma. According to the research findings in this paper, our main results give estimates for the modulus and the argument for the entire class of Carathéodory functions. As applications, we give several extensions of Julia-Wolf-Carathéodory Lemma in a half-strip and show that our results are sharp.

Keywords: schwarz lemma, Julia-wolf-caratéodory lemma, analytic function, normalization condition, caratéodory function

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: equivalent martingale measure, European put option, girsanov theorem, martingales, monte carlo method, option price valuation formula

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Authors: Tuula Heinonen, Wilhelm Gaus

Abstract:

At present safety, assessment starts with animal tests although their predictivity is often poor. Even after extended human use experimental data are often judged as the core information for risk assessment. However, the best opportunity to generate true evidence is to match all available information. Cross matching methodology combines the different fields of knowledge and types of data (e.g. in-vitro and in-vivo experiments, clinical observations, clinical and epidemiological studies, and daily life observations) and gives adequate weight to individual findings. To achieve a consolidated outcome, the information from all available sources is analysed and compared with each other. If single pieces of information fit together a clear picture becomes visible. If pieces of information are inconsistent or contradictory careful consideration is necessary. 'Cross' can be understood as 'orthographic' in geometry or as 'independent' in mathematics. Results coming from different sources bring independent and; therefore, they result in new information. Independent information gives a larger contribution to evidence than results coming repeatedly from the same source. A successful example of cross matching is the assessment of Ginkgo biloba where we were able to come to the conclusive result: Ginkgo biloba leave extract is well tolerated and safe for humans.

Keywords: cross-matching, human use, safety assessment, Ginkgo biloba leave extract

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Authors: Yin-Yann Chen, Jia-Ying Li

Abstract:

Assembly line balancing problems can be categorized into one-sided, two-sided, and multi-manned ones by using the number of operators deployed at workstations. This study explores the balancing problem of a resource-constrained assembly line with multi-manned workstations. Resources include machines or tools in assembly lines such as jigs, fixtures, and hand tools. A mathematical programming model was developed to carry out decision-making and planning in order to minimize the numbers of workstations, resources, and operators for achieving optimal production efficiency. To improve the solution-finding efficiency, a genetic algorithm (GA) and a simulated annealing algorithm (SA) were designed and developed in this study to be combined with a practical case in car making. Results of the GA/SA and mathematics programming were compared to verify their validity. Finally, analysis and comparison were conducted in terms of the target values, production efficiency, and deployment combinations provided by the algorithms in order for the results of this study to provide references for decision-making on production deployment.

Keywords: heuristic algorithms, line balancing, multi-manned workstation, resource-constrained

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Authors: Nataliya G. Olkhovik

Abstract:

Nowadays in the system of Russian higher medical education there have been undertaken initiatives that resulted in focusing on the resources of e-learning in teaching foreign languages. Obviously, the face-to-face communication in foreign languages bears much more advantages in terms of effectiveness in comparison with the potential of e-learning. Thus, we’ve faced the necessity of strengthening the capacity of e-learning via integration of active methods into the process of teaching foreign languages, such as project activity of students. Successful project activity of students should involve the following components: monitoring, control, methods of organizing the student’s activity in foreign languages, stimulating their interest in the chosen project, approaches to self-assessment and methods of raising their self-esteem. The contemporary methodology assumes the project as a specific method, which activates potential of a student’s cognitive function, emotional reaction, ability to work in the team, commitment, skills of cooperation and, consequently, their readiness to verbalize ideas, thoughts and attitudes. Verbal activity in the foreign language is a complex conception that consolidates both cognitive (involving speech) capacity and individual traits and attitudes such as initiative, empathy, devotion, responsibility etc. Once we organize the project activity by the means of e-learning within the ‘Foreign language’ discipline we have to take into consideration all mentioned above characteristics and work out an effective way to implement it into the teaching practice to boost its educational potential. We have integrated into the e-platform Moodle the module of project activity consisting of the following blocks of tasks that lead students to research, cooperate, strive to leadership, chase the goal and finally verbalize their intentions. Firstly, we introduce the project through activating self-activity of students by the tasks of the phase ‘Preparation of the project’: choose the topic and justify it; find out the problematic situation and its components; set the goals; create your team, choose the leader, distribute the roles in your team; make a written report on grounding the validity of your choices. Secondly, in the ‘Planning the project’ phase we ask students to represent the analysis of the problem in terms of reasons, ways and methods of solution and define the structure of their project (here students may choose oral or written presentation by drawing up the claim in the e-platform about their wish, whereas the teacher decides what form of presentation to prefer). Thirdly, the students have to design the visual aids, speech samples (functional phrases, introductory words, keywords, synonyms, opposites, attributive constructions) and then after checking, discussing and correcting with a teacher via the means of Moodle present it in front of the audience. And finally, we introduce the phase of self-reflection that aims to awake the inner desire of students to improve their verbal activity in a foreign language. As a result, by implementing the project activity into the e-platform and project activity, we try to widen the frameworks of a traditional lesson of foreign languages through tapping the potential of personal traits and attitudes of students.

Keywords: active methods, e-learning, improving verbal activity in foreign languages, personal traits and attitudes

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Authors: Gilbert Makanda, Roelf Sypkens

Abstract:

A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: differential equations, knowledge acquisition, least squares nonlinear, dynamical systems

Procedia PDF Downloads 364