Search results for: mathematical theory

Authors: Karen K. Perez-Ramirez, Genevieve Dupont, Virginia Gonzalez-Velez

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Pancreatic alpha-cells participate on glucose regulation together with beta cells. They release glucagon hormone when glucose level is low to stimulate gluconeogenesis from the liver. As other excitable cells, alpha cells generate Ca2+ and metabolic oscillations when they are stimulated. It is known that the glucose level can trigger or silence this activity although it is not clear how this occurs in normal and diabetic people. In this work, we propose an electric-metabolic mathematical model implemented in Matlab to study the effect of different glucose levels on the electrical response and Ca2+ oscillations of an alpha cell. Our results show that Ca2+ oscillations appear in opposite phase with metabolic oscillations in a window of glucose values. The model also predicts a direct relationship between the level of glucose and the intracellular adenine nucleotides showing a self-regulating pathway for the alpha cell.

Keywords: Ca2+ oscillations, mathematical model, metabolic oscillations, pancreatic alpha cell

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Authors: Toru Shionoya, Yosuke Kurihara, Takashi Kaburagi, Kajiro Watanabe

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Mass-produced bidirectional microphones have attractive characteristics. They work as a microphone as well as a sensor with high gain over a wide frequency range; they are also highly reliable and economical. We present novel multiple functional uses of the microphones. A mathematical model for explaining the high-pass-filtering characteristics of bidirectional microphones was presented. Based on the model, the characteristics of the microphone were investigated, and a novel use for the microphone as a sensor with a wide frequency range was presented. In this study, applications for using the microphone as a security sensor and a human biosensor were introduced. The mathematical model was validated through experiments, and the feasibility of the abovementioned applications for security monitoring and the biosignal monitoring were examined through experiments.

Keywords: bidirectional microphone, low-frequency, mathematical model, frequency response

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Authors: Nathaporn Areerachakul

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In this study, the adsorption capacity of GAC with metsulfuron methyl was evaluated by using adsorption equilibrium and a fixed bed. Mathematical modelling was also used to simulate the GAC adsorption behavior. Adsorption equilibrium experiment of GAC was conducted using a constant concentration of metsulfuron methyl of 10 mg/L. The purpose of this study was to find the single component equilibrium concentration of herbicide. The adsorption behavior was simulated using the Langmuir, Freundlich, and Sips isotherm. The Sips isotherm fitted the experimental data reasonably well with an error of 6.6 % compared with 15.72 % and 7.07% for the Langmuir isotherm and Freudrich isotherm. Modelling using GAC adsorption theory could not replicate the experimental results in fixed bed column of 10 and 15 cm bed depths after a period more than 10 days of operation. This phenomenon is attributed to the formation of micro-organism (BAC) on the surface of GAC in addition to GAC alone.

Keywords: isotherm, adsorption equilibrium, GAC, metsulfuron methyl

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Authors: Laurence Doremus

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Freud as the builder of psychoanalysis as a discipline had created the science with Carl Gustav Jung (1875-1961), a psychiatry specialist from Zurich who was very important in the Freudian theory. The knowledge about the foundation of psychoanalysis is often focused on the influence of the works from Breuer or Charcot in the Freudian praxis, at least at the beginning of his career, and Jung's influence is often under-estimated. The paper focuses on the importance of the Jungian contributions in Freud's theories at the beginning of the creation of the discipline in the 1910s. We often meet Jungian schools on the first hand and Freudian schools, on the other hand in the academic field, but the Freudian field has to admit the importance of the Jungian theories in Freudian science. And also, the dialectical energy which appears in the letters exchanged between both of the fathers of psychoanalysis is important to understand the foundations of Freud Theory. That's why the paper will analyze in detail the correspondence between them in an epistemological and historical approach. Effectively the letters were translated and published (in French but also in English and other languages) lately in history and are still not well knew by the researchers in the psychoanalytical field. We well explain how Freud was helped by Jung despite his desire to build the theory. We analyze how the second topic named 'unconscious, preconscious, and conscious', is the result of the first topic that Jung built with Freud. The paper is a contribution to the knowledge we should have about the intense friendship between the two protagonists.

Keywords: Carl Gustav Jung, correspondence, Freud's letters, psychoanalytic theory

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Authors: Robert L. Burdett, Bayan Bevrani

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Analytical techniques for measuring and planning railway capacity expansion activities have been considered in this article. A preliminary mathematical framework involving track duplication and section sub divisions is proposed for this task. In railways, these features have a great effect on network performance and for this reason they have been considered. Additional motivations have also arisen from the limitations of prior models that have not included them.

Keywords: capacity analysis, capacity expansion, railways, track sub division, track duplication

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Authors: Harry G. Segal

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The idea of the “self” has been essential ever since the early modern period in western culture, especially since the development of psychotherapy, but advances in neuroscience and cognitive theory challenge traditional notions of the self. More specifically, neuroanatomists have found no location of “the self” in the brain; instead, consciousness has been posited to be a rapid combination of perception, memory, anticipation of future events, and judgment. In this paper, a theoretical model is presented to address these neuroanatomical findings and to revise the historical understanding of “selfhood” in the practice of psychotherapy.

Keywords: the self, psychotherapy, the self and the brain

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Authors: Ledeza Jordan Babiano

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Translating statements into mathematical notations is one of the processes in word problem-solving. However, based on the literature, students still have difficulties with this skill. The purpose of this study was to investigate the translation errors of the students when they translate algebraic word problems into mathematical structures and locate the errors via the lens of the Translation-Verification Model. Moreover, this qualitative research study employed content analysis. During the data-gathering process, the students were asked to answer a six-item algebra word problem questionnaire, and their answers were analyzed by experts through blind coding using the Translation-Verification Model to determine their translation errors. After this, a focus group discussion was conducted, and the data gathered was analyzed through thematic analysis to determine the causes of the students’ translation errors. It was found out that students’ prevalent error in translation was the interpretation error, which was situated in the Attribute construct. The emerging themes during the FGD were: (1) The procedure of translation is strategically incorrect; (2) Lack of comprehension; (3) Algebra concepts related to difficulty; (4) Lack of spatial skills; (5) Unprepared for independent learning; and (6) The content of the problem is developmentally inappropriate. These themes boiled down to the major concept of independent learning preparedness in solving mathematical problems. This concept has subcomponents, which include contextual and conceptual factors in translation. Consequently, the results provided implications for instructors and professors in Mathematics to innovate their teaching pedagogies and strategies to address translation gaps among students.

Keywords: mathematical structure, algebra word problems, translation, errors

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Authors: Chih-Ping Chen

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Despite the increasing popularity of and interest in mobile games, there has been little research that evaluates gender differences in users’ actual preferences for mobile game content, and the factors that influence entertainment and mobile-learning habits. To fill this void, this study examines different gender users’ experience of mobile English learning game adoption in order to identify the areas of development in Taiwan, using Uses and Gratification Theory, Expectation Confirmation Theory and experiential value. The integration of these theories forms the basis of an extended research concept. Users’ responses to questions about cognitive perceptions, confirmation, gratifications and continuous use were collected and analyzed with various factors derived from the theories.

Keywords: expectation confirmation theory, experiential value, gender difference, mobile game, uses and gratification

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Authors: Francys Souza, Alberto Ohashi, Dorival Leao

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We present a general solution for finding the ε-optimal controls for non-Markovian stochastic systems as stochastic differential equations driven by Brownian motion, which is a problem recognized as a difficult solution. The contribution appears in the development of mathematical tools to deal with modeling and control of non-Markovian systems, whose applicability in different areas is well known. The methodology used consists to discretize the problem through a random discretization. In this way, we transform an infinite dimensional problem in a finite dimensional, thereafter we use measurable selection arguments, to find a control on an explicit form for the discretized problem. Then, we prove the control found for the discretized problem is a ε-optimal control for the original problem. Our theory provides a concrete description of a rather general class, among the principals, we can highlight financial problems such as portfolio control, hedging, super-hedging, pairs-trading and others. Therefore, our main contribution is the development of a tool to explicitly the ε-optimal control for non-Markovian stochastic systems. The pathwise analysis was made through a random discretization jointly with measurable selection arguments, has provided us with a structure to transform an infinite dimensional problem into a finite dimensional. The theory is applied to stochastic control problems based on path-dependent stochastic differential equations, where both drift and diffusion components are controlled. We are able to explicitly show optimal control with our method.

Keywords: dynamic programming equation, optimal control, stochastic control, stochastic differential equation

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Authors: E. Fredrick Rice

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Over the past three decades, a substantial body of academic literature has asserted that the pressure to maintain household income can negatively affect the personal well-being of breadwinners. Given that scholars have failed to thoroughly explore this phenomenon with breadwinners who are also business owners, theory has been underdeveloped in the entrepreneurial context. To identify the most appropriate theories to apply to entrepreneurs, the current paper utilized two approaches. First, a comprehensive bibliographic analysis was conducted focusing on works at the intersection of breadwinner status and well-being. Co-authorship and journal citation patterns highlighted relative resource theory as a boundary spanning approach with promising applications in the entrepreneurial space. To build upon this theory, regression analysis was performed using data from the Panel Study of Entrepreneurial Dynamics (PSED). Empirical results showed evidence for the effects of breadwinner status and household income on entrepreneurial well-being. Further, the findings suggest that it is not merely income or job status that predicts well-being, but one’s relative financial contribution compared to that of one’s non-breadwinning organizationally employed partner. This paper offers insight into how breadwinner status can be studied in relation to the entrepreneurial personality.

Keywords: breadwinner, entrepreneurship, household income, well-being.

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Authors: Betty Johanna Garzon Rozo, Jonathan Crook, Fernando Moreira

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Operational risk losses are heavy tailed and are likely to be asymmetric and extremely dependent among business lines/event types. We propose a new methodology to assess, in a multivariate way, the asymmetry and extreme dependence between severity distributions, and to calculate the capital for Operational Risk. This methodology simultaneously uses (i) several parametric distributions and an alternative mix distribution (the Lognormal for the body of losses and the Generalized Pareto Distribution for the tail) via extreme value theory using SAS®, (ii) the multivariate skew t-copula applied for the first time for operational losses and (iii) Bayesian theory to estimate new n-dimensional skew t-copula models via Markov chain Monte Carlo (MCMC) simulation. This paper analyses a newly operational loss data set, SAS Global Operational Risk Data [SAS OpRisk], to model operational risk at international financial institutions. All the severity models are constructed in SAS® 9.2. We implement the procedure PROC SEVERITY and PROC NLMIXED. This paper focuses in describing this implementation.

Keywords: operational risk, loss distribution approach, extreme value theory, copulas

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Authors: Magda Cepeda, Frances Hodgson, Ann Jopson

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There are different barriers people face when choosing to cycle for commuting purposes. This study examined the role of psycho-social factors predicting the intention to cycle to commute in Mexico City. An extended version of the theory of planned behaviour was developed and utilized with a simple random sample of 401 road users. We applied exploratory and confirmatory factor analysis and after identifying five factors, a structural equation model was estimated to find the relationships among the variables. The results indicated that cycling attributes, attitudes to cycling, social comparison and social image and prestige were the most important factors influencing intention to cycle. Although the results from this study are specific to Mexico City, they indicate areas of interest to transportation planners in other regions especially in those cities where intention to cycle its linked to its perceived image and there is political ambition to instigate positive cycling cultures. Moreover, this study contributes to the current literature developing applications of the Theory of Planned Behaviour.

Keywords: cycling, latent variable model, perception, theory of planned behaviour

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Authors: Fadi Awawdeh

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In this work, we highlight the key concepts in using semigroup theory as a methodology used to construct efficient formulas for solving inverse problems. The proposed method depends on some results concerning integral equations. The experimental results show the potential and limitations of the method and imply directions for future work.

Keywords: identification problems, semigroup theory, methods for inverse problems, scientific computing

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Authors: Samar M. Alqhtani, Suhuai Luo, Brian Regan

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Data fusion technology can be the best way to extract useful information from multiple sources of data. It has been widely applied in various applications. This paper presents a data fusion approach in multimedia data for event detection in twitter by using Dempster-Shafer evidence theory. The methodology applies a mining algorithm to detect the event. There are two types of data in the fusion. The first is features extracted from text by using the bag-ofwords method which is calculated using the term frequency-inverse document frequency (TF-IDF). The second is the visual features extracted by applying scale-invariant feature transform (SIFT). The Dempster - Shafer theory of evidence is applied in order to fuse the information from these two sources. Our experiments have indicated that comparing to the approaches using individual data source, the proposed data fusion approach can increase the prediction accuracy for event detection. The experimental result showed that the proposed method achieved a high accuracy of 0.97, comparing with 0.93 with texts only, and 0.86 with images only.

Keywords: data fusion, Dempster-Shafer theory, data mining, event detection

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Authors: Shittu Akinpelu, Issac Popoola

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The compound NbRhGe has been predicted to be a semiconductor with excellent mechanical properties. It is an indirect band gap material. The potential of NbRhGe for non-volatile data storage via element addition is being studied using the Density Functional Theory (DFT). Preliminary results on the electronic and magnetic properties are suggestive for their application in spintronic.

Keywords: half-metals, Heusler compound, semiconductor, spintronic

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Authors: Yasaman Azarmjoo

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Since ancient times, it has been said that mathematics is the mother of all sciences and the foundation of basic concepts in every field and profession. It would be great if, after learning this subject, we could enable students to create games and activities based on the same mathematical concepts. This article explores the design of various mathematical activities in the form of games, utilizing different mathematical topics such as algebra, equations, binary systems, and one-to-one correspondence. The theoretical significance of this article lies in uncovering alternative approaches to teaching and learning mathematics. By employing creative and interactive methods such as game design, it challenges the traditional perception of mathematics as a difficult and laborious subject. The theoretical significance of this article lies in demonstrating that mathematics can be made more accessible and enjoyable, which can result in heightened interest and engagement in the subject. In general, this article reveals another aspect of mathematics.

Keywords: playing with mathematics, algebra and equations, binary systems, one-to-one correspondence

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Authors: Krisstalova Dana, Mazal Jan

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This article deals with geographical conditions in terrain and their effect on the movement of vehicles, their effect on speed and safety of movement of people and vehicles. Finding of the optimal routes outside the communication is studied in the army environment, but it occur in civilian as well, primarily in crisis situation, or by the provision of assistance when natural disasters such as floods, fires, storms etc., have happened. These movements require the optimization of routes when effects of geographical factors should be included. The most important factor is the surface of a terrain. It is based on several geographical factors as are slopes, soil conditions, micro-relief, a type of surface and meteorological conditions. Their mutual impact has been given by coefficient of deceleration. This coefficient can be used for the commander`s decision. New approaches and methods of terrain testing, mathematical computing, mathematical statistics or cartometric investigation are necessary parts of this evaluation.

Keywords: movement in a terrain, geographical factors, surface of a field, mathematical evaluation, optimization and searching paths

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Authors: Nitin Ghule, S. G. Taji

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A mathematical model of hot-wall condensers used in refrigerators is presented. The model predicts the heat transfer characteristics of condenser and the effects of various design and operating parameters on condenser tube length and capacity. A finite element approach was used to model the condenser. The condenser tube is divided into elemental units, with each element consisting of adhesive tape, refrigerant tube and outer metal sheet. The heat transfer characteristics of each section are then analyzed by considering the heat transfer through the tube wall, tape and the outer sheet. Variations in inner heat transfer coefficient and pressure drop are considered depending on temperature, fluid phase, type of flow and orientation of tube. Variation in outer heat transfer coefficient is also taken into account. Various materials were analysed for the tube, tape and outer sheet.

Keywords: condenser, domestic refrigerator, heat transfer, mathematical model

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Authors: Anne Gibbons

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Both inside and outside of academia, people have sought to understand the “sense of place” of various regions, many times over and for many different reasons. The concept of regional identity is highly complex and surrounded by considerable contention. There are multiple bodies of research on regional identity theory in many different disciplines and even across sub-disciplinary classifications. Each discipline takes a slightly different angle or perspective on regional identity, resulting in a fragmented body of work on this topic overall. There is a need to consolidate this body of increasingly fragmented theory through interdisciplinary integration. For the purpose of this study, the province of Saskatchewan will serve as an exemplar for exploring regional identity in a concrete context. Saskatchewan can be thought of as a ‘functional region,’ with clear boundaries and clear residency, from which regional identity can be studied. This thesis shares the outcomes of a qualitative study grounded in a series of group interviews with askatchewan residents, from which it is concluded that the use of interdisciplinary theory is an appropriate approach to the study of regional identity. Regional identity cannot be compartmentalized; it is a web of characteristics, attributes, and feelings that are inextricably linked. The thesis thus concludes by offering lessons learned about how we might better understand regional identity, as illuminated through both interdisciplinary theory and the lived experiences and imaginations of people living in the region of Saskatchewan.

Keywords: interdisciplinary, regional identity, Saskatchewan, tourism studies

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Authors: Pontus Backstrom

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In the educational literature on peer effects, attention has been brought to the fact that the mechanisms creating peer effects are still to a large extent hidden in obscurity. The hypothesis in this study is that the Frame Factor Theory can be used to explain these mechanisms. At heart of the theory is the concept of “time needed” for students to learn a certain curricula unit. The relations between class-aggregated time needed and the actual time available, steers and hinders the actions possible for the teacher. Further, the theory predicts that the timing and pacing of the teachers’ instruction is governed by a “criterion steering group” (CSG), namely the pupils in the 10th-25th percentile of the aptitude distribution in class. The class composition hereby set the possibilities and limitations for instruction, creating peer effects on individual outcomes. To test if the theory can be applied to the issue of peer effects, the study employs multilevel structural equation modelling (M-SEM) on Swedish TIMSS 2015-data (Trends in International Mathematics and Science Study; students N=4090, teachers N=200). Using confirmatory factor analysis (CFA) in the SEM-framework in MPLUS, latent variables are specified according to the theory, such as “limitations of instruction” from TIMSS survey items. The results indicate a good model fit to data of the measurement model. Research is still in progress, but preliminary results from initial M-SEM-models verify a strong relation between the mean level of the CSG and the latent variable of limitations on instruction, a variable which in turn have a great impact on individual students’ test results. Further analysis is required, but so far the analysis indicates a confirmation of the predictions derived from the frame factor theory and reveals that one of the important mechanisms creating peer effects in student outcomes is the effect the class composition has upon the teachers’ instruction in class.

Keywords: compositional effects, frame factor theory, peer effects, structural equation modelling

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Authors: Rawaa El Ayoubi

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Many researchers, academics and practitioners have developed leadership theories during the 20th century. This substantial effort has built more leadership theories, generating considerable organisational research on leadership models in contemporary literature. This paper explores the stages and drivers of leadership theory evolution based on the researcher’s personal conclusions and review of leadership theories. The purpose of this paper is to create a Leadership Process Model (LPM) that can provide guidance in dealing with the key challenges within the organisation. This integrative model of organisational leadership is based on inner meaning, leader values and vision. It further addresses the relationships between leadership theory, practice and development, exploring why challenges exist within the field of leadership theory and how these challenges can be mitigated.

Keywords: leadership challenges, leadership process model, leadership |theories, organisational leadership, paradigm development

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Authors: M. Y. Ismail, M. Inam, A. F. M. Zain, N. Misran

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Progressive phase distribution is an important consideration in reflect array antenna design which is required to form a planar wave in front of the reflect array aperture. This paper presents a detailed mathematical model in order to determine the required reflection phase values from individual element of a reflect array designed in Ku-band frequency range. The proposed technique of obtaining reflection phase can be applied for any geometrical design of elements and is independent of number of array elements. Moreover the model also deals with the solution of reflect array antenna design with both centre and off-set feed configurations. The theoretical modeling has also been implemented for reflect arrays constructed on 0.508 mm thickness of different dielectric substrates. The results show an increase in the slope of the phase curve from 4.61°/mm to 22.35°/mm by varying the material properties.

Keywords: mathematical modeling, progressive phase distribution, reflect array antenna, reflection phase

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Authors: Lian Yang

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Object-oriented programming (OOP) is the dominant programming paradigm in today’s software industry and it has literally enabled average software developers to develop millions of commercial strength software applications in the era of INTERNET revolution over the past three decades. On the other hand, the lack of strict mathematical model and domain constraint features at the language level has long perplexed the computer science academia and OOP engineering community. This situation resulted in inconsistent system qualities and hard-to-understand designs in some OOP projects. The difficulties with regards to fix the current situation are also well known. Although the power of OOP lies in its unbridled flexibility and enormously rich data modeling capability, we argue that the ambiguity and the implicit facade surrounding the conceptual model of a class and an object should be eliminated as much as possible. We listed the five major usage of class and propose to separate them by proposing new language constructs. By using well-established theories of set and FSM, we propose to apply certain simple, generic, and yet effective constraints at OOP language level in an attempt to find a possible solution to the above-mentioned issues regarding OOP. The goal is to make OOP more theoretically sound as well as to aid programmers uncover warning signs of irregularities and domain-specific issues in applications early on the development stage and catch semantic mistakes at runtime, improving correctness verifiability of software programs. On the other hand, the aim of this paper is more practical than theoretical.

Keywords: new language constructs, set theory, FSM theory, user defined value type, function groups, membership qualification attribute (MQA), check-constraint (CC)

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Authors: Ruth Donkoh, Wing On Lee, Solomon A. Boateng, Portia Oware Twerefoo, Josephine Donkor

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In this paper we defend the value of theories and approaches to educational policy and planning in enhancing the educational developments in Ghana. This mission is achieved by enumerating the recent educational developments in Ghana and juxtaposing it with some educational theories, approaches to policy making, and policy planning to see if the educational developments conform with the theory principles as well as policy making and planning processes. Data collection for the research was made through textual analysis of policy documents as well as review of relevant literatures. The findings reveled that educational developments in Ghana are unable to attain its objectives due to the policies not conforming with the policy formation and planning principles. In addition, was that education planning in Ghana does not follow the policy-administration dichotomy theory principles and likewise the distribution of educational needs goes contrary to the equity theory. We recommend that educational policies in Ghana should be in conformity with the principles of theories as well as the approaches to educational policy making and planning to help meet the needs of learners, attain educational quality, and to help in the accomplishment of educational development objectives.

Keywords: Ghana education, equity theories, politics- administration dichotomy theory, educational policies, educational planning

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Authors: Sahar Dehghan, Yeganeh Mousavi Jahromi, Ghahraman Abdoli

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Since tax revenues are one of the most important sources of government revenue, it is essential to consider increasing taxpayers' compliance. One of the factors that can affect the taxpayers' compliance is the structure of the crimes and incentives envisaged in the tax law. In this research, by using the 'prospect theory', the effects of changes in the rate of crimes and the tax incentive in the direct tax law on the taxpayer’s compliance behavior have been investigated. To determine the preferences and preferences of taxpayer’s in the business sector and their degree of sensitivity to fines and incentives, a questionnaire with mixed gamble structure is designed. Estimated results using the Hierarchical Bayesian method indicate that the taxpayer’s that have been tested in this study are more sensitive to the incentives in the direct tax law, and the tax administration can use this to increase the level of collected tax and increase the level of compliance.

Keywords: tax compliance, prospect theory, value function, mixed gamble

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Authors: Danika Tynes

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Telehealth is a promising advancement in health care, though there are certain conditions under which telehealth has a greater chance of success. This research sought to further the understanding of what conditions compel the success of telehealth adoption at the systems level applying Diffusion of Innovations (DoI) theory (Rogers, 1962). System-level indicators were selected to represent four components of DoI theory (relative advantage, compatibility, complexity, and observability) and regressed on 5 types of telehealth (teleradiology, teledermatology, telepathology, telepsychology, and remote monitoring) using multiple logistic regression. The analyses supported relative advantage and compatibility as the strongest influencers of telehealth adoption, remote monitoring in particular. These findings help to quantitatively clarify the factors influencing the adoption of innovation and advance the ability to make recommendations on the viability of state telehealth adoption. In addition, results indicate when DoI theory is most applicable to the understanding of telehealth diffusion. Ultimately, this research may contribute to more focused allocation of scarce health care resources through consideration of existing state conditions available foster innovation.

Keywords: adoption, diffusion of innovation theory, remote monitoring, system-level indicators

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Authors: Lely A. Luengas, Pedro R. Vizcaya, Giovanni Sánchez

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In this paper, a methodology is presented to obtain the Static Alignment Model for any transtibial amputee person. The proposed methodology starts from experimental data collected on the Hospital Militar Central, Bogotá, Colombia. The effects of transtibial prosthesis malalignment on amputees were measured in terms of joint angles, center of pressure (COP) and weight distribution. Some statistical tools are used to obtain the model parameters. Mathematical predictive models of prosthetic alignment were created. The proposed models are validated in amputees and finding promising results for the prosthesis Static Alignment. Static alignment process is unique to each subject; nevertheless the proposed methodology can be used in each transtibial amputee.

Keywords: information theory, prediction model, prosthetic alignment, transtibial prosthesis

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Authors: Arnold M. Brener, Lesbek Tashimov, Ablakim S. Muratov

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The paper deals with the special model for coagulation kernels which represents new control parameters in the Smoluchowski equation for binary aggregation. On the base of the model the new approach to evaluating aggregative stability of disperse systems has been submitted. With the help of this approach the simple estimates for aggregative stability of various types of hydrophilic nano-suspensions have been obtained.

Keywords: aggregative stability, coagulation kernels, disperse systems, mathematical model

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Authors: Peter Akayuure, Michael Johnson Nabie

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Similar to many colonized nations in the world, one indelible mark left by colonial masters after Ghana’s independence in 1957 has been the fact that many contexts used to teach statistics and probability concepts are often alien and do not resonate with the social domain of our indigenous Ghanaian child. This has seriously limited the understanding, discoveries, and applications of mathematics for national developments. With the recent curriculum demands of making the Ghanaian child mathematically literate, this qualitative study involved video recordings and mathematical analysis of play sessions of an indigenous girl game called Ampe with the aim to demystify the concepts in probability theorem, which is applied in mathematics related fields of study. The mathematical analysis shows that the game of Ampe, which is widely played by school girls in Ghana, is suitable for learning concepts of the probability theorems. It was also revealed that as a girl game, the use of Ampe provides good lessons to educators, textbook writers, and teachers to rethink about the selection of mathematics tasks and learning contexts that are sensitive to gender. As we undertake to transform teacher education and student learning, the use of indigenous games should be critically revisited.

Keywords: Ampe, mathematical analysis, probability theorem, Ghanaian girl game

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Authors: Sperisa Distantina, Rieke Ulfha Noviyanti, Sri Sutriyani, Fadilah Fadilah, Mujtahid Kaavessina

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In this research, carrageenan extracted from seaweed Eucheuma cottonii was mixed with polyvinyl alcohol (PVA) and then crosslinked using glutaraldehyde (GA). The obtained hydrogel films were applied to control the drug release rate of paracetamol. The aim of this research was to develop a mathematical model that can be used to describe the mass transfer rate of paracetamol from the hydrogel film into buffer solution. The effect of weight ratio carrageenan-PVA (5: 0, 1: 0.5, 1: 1, 1: 2, 0: 5) on the parameters of the mathematical model was investigated also. Based on the experimental data, the proposed mathematical model could describe the mass transfer rate of paracetamol. The weight ratio of carrageenan-PVA greatly affected the amount of paracetamol absorbed in the hydrogel film and the mass transfer rate of paracetamol.

Keywords: carrageenan-PVA, crosslinking, glutaraldehyde, hydrogel, paracetamol, mass transfer

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