Search results for: classical predicate calculus

Authors: T. J. Stepien, L. T. Stepien

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This abstract concerns an extremely fundamental issue. Namely, the fundamental problem of science is the issue of consistency. In this abstract, we present the theorem saying that the classical calculus of quantifiers is inconsistent in the traditional sense. At the beginning, we introduce a notation, and later we remind the definition of the consistency in the traditional sense. S1 is the set of all well-formed formulas in the calculus of quantifiers. RS1 denotes the set of all rules over the set S1. Cn(R, X) is the set of all formulas standardly provable from X by rules R, where R is a subset of RS1, and X is a subset of S1. The couple < R,X > is called a system, whenever R is a subset of RS1, and X is a subset of S1. Definition: The system < R,X > is consistent in the traditional sense if there does not exist any formula from the set S1, such that this formula and its negation are provable from X, by using rules from R. Finally, < R0+, L2 > denotes the classical calculus of quantifiers, where R0+ consists of Modus Ponens and the generalization rule. L2 is the set of all formulas valid in the classical calculus of quantifiers. The Main Result: The system < R0+, L2 > is inconsistent in the traditional sense.

Keywords: classical calculus of quantifiers, classical predicate calculus, generalization rule, consistency in the traditional sense, Modus Ponens

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Authors: Jorge Lopez

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In this work, we introduce fractional calculus in order to study the dynamics of a damped multistory building with some symmetry. Initially we make a review of the dynamics of a free and damped multistory building. Then we introduce those concepts of fractional calculus that will be involved in our study. It has been noticed that fractional calculus provides models with less parameters than those based on classical calculus. In particular, a damped classical oscilator is more naturally described by using fractional derivatives. Accordingly, we model our multistory building as a set of coupled fractional oscillators and compare its dynamics with the results coming from traditional methods.

Keywords: coupled oscillators, fractional calculus, fractional oscillator, structural dynamics

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Authors: Stephen Kirkup

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This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: boundary element method, Laplace’s equation, vector calculus, simulation, education

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Authors: Paola Cattabriga

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According to Gödel’s first incompleteness argument it is possible to construct a formally undecidable proposition in Principia mathematica, a statement that, although true, turns out to be neither provable nor refutable for the system, making therefore incomplete any formal system suitable for the arithmetic of integers. Its features and limitation effects are today widespread basics throughout whole scientific thought. This article brings Gödel’s achievement into question by the definition of the refutability predicate as a number-theoretical statement. We develop proof of invalidity of Theorem VI in Gödel’s 1931, the so-called Gödel’s first incompleteness theorem, in two steps: defining refutability within the same recursive status as provability and showing that as a consequence propositions (15) and (16), derived from definition 8.1 in Gödel’s 1931, are false and unacceptable for the system. The achievement of their falsity blocks the derivation of Theorem VI, which turns out to be therefore invalid, together with all the depending theorems. This article opens up thus new perspectives for mathematical research and for the overall scientific reasoning.

Keywords: Gödel numbering, incompleteness, provability predicate, refutability predicate

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Authors: Khaled I. Nawafleh

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In this work, we apply the method of Hamilton-Jacobi to obtain solutions of Hamiltonian systems in classical mechanics with two certain structures: the first structure plays a central role in the theory of time-dependent Hamiltonians, whilst the second is used to treat classical Hamiltonians, including dissipation terms. It is proved that the generalization of problems from the calculus of variation methods in the nonstationary case can be obtained naturally in Hamilton-Jacobi formalism. Then, another expression of geometry of the Hamilton Jacobi equation is retrieved for Hamiltonians with time-dependent and frictional terms. Both approaches shall be applied to many physical examples.

Keywords: Hamilton-Jacobi, time dependent lagrangians, dissipative systems, variational principle

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Authors: Tshaudi Motsima

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Class attendance is key at all levels of education. At tertiary level many students develop a tendency of not attending all classes without being aware of the repercussions of not attending all classes. It is important for all students to attend all classes as they can receive first-hand information and they can benefit more. The student who attends classes is likely to perform better academically than the student who does not. The aim of this paper is to assess the relationship between class attendance and academic performance of industrial engineering students. The data for this study were collected through the attendance register of students and the other data were accessed from the Integrated Tertiary Software and the Higher Education Data Analyzer Portal. Data analysis was conducted on a sample of 93 students. The results revealed that students with medium predicate scores (OR = 3.8; p = 0.027) and students with low predicate scores (OR = 21.4, p < 0.001) were significantly likely to attend less than 80% of the classes as compared to students with high predicate scores. Students with examination performance of less than 50% were likely to attend less than 80% of classes than students with examination performance of 50% and above, but the differences were not statistically significant (OR = 1.3; p = 0.750).

Keywords: class attendance, examination performance, final outcome, logistic regression

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Authors: R. Pargas, M. Reba

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Since 2006, the School of Computing and the Department of Mathematical Sciences have collaborated on several industry and NSF grants to develop new uses of technology in teaching and learning. Clemson University’s Creative Inquiry Program allowed computer science and mathematics students to earn credit each semester for participating in seminars which introduced them to new areas for independent research. We will discuss how the development of three interactive instructional apps for Calculus resulted not only in a useful product, but also in unique educational benefits for both the computer science students and the mathematics students, graduate and undergraduate, involved in the development process.

Keywords: calculus, apps, programming, mathematics

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Authors: Yaqing Hu

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This paper puts forward a syntactic analysis involving multidominance and rightward movement in Chinese bi-comparatives, as in 'Yuehan bi Mali gao (John is taller than Mary).' It is argued here that the predicate of comparison is a shared constituent in two small clauses, namely one for the target and one for the standard; and then it moves rightward to form a degree phrase with the comparative morpheme. This proposal comes from four aspects. First, the example above can also be expressed in this way, 'A: Yuehan he Mali, shui gao? (John and Mary, who is taller?) B: Yuehan gao./Yuehan geng gao. (John is taller).' This shows that the gradable adjective is predicated of the target. In addition, according to a constraint on Chinese bi-comparatives, namely the target and the standard must be arguments of the predicate simultaneously, it is not unreasonable to assume that the gradable adjective may also be predicated of the standard. Second, subcomparatives are totally disallowed in Chinese, as in '*zhe-zhang zhuozi bi zhe-zhang yizi kuan chang. (This table is longer than this chair is wide.)' In order to save it from ungrammaticality, the target and the standard should be compared along the same dimension denoted by the gradable adjective. It may follow that in Chinese comparatives, having equal roles in the same eventuality, the target and the standard bear the same thematic relationship with the predicate of comparison. Third, verb-copy can appear in Chinese bi-comparatives, as in 'Yuehan qi ma bi Mali qi ma qi de kuai. (John rides horses faster than Mary does.)' The predicate qi seems to form a small clause with both the target and the standard. This might be supporting evidence that both the target and the standard share the predicate of comparison. Fourth, Chinese comparatives do have comparative morphemes, as in 'Yuehan bi Mali geng gao. (John is taller than Mary)', which is semantically equivalent to the first example above. Thus, it follows that one feature of Chinese comparative morphemes is that they can remain overt or covert in the syntax, which will not affect semantics. This further shows that comparative morphemes in bi-comparatives may not be able to saturate the degree argument denoted by the predicate of comparison due to its optionality in the structure. These four aspects present a challenge to the Direct Analysis used in Chinese comparatives since this approach would presume that the target and the standard somehow show independency with the predicate in the syntax. Meanwhile, this study also rejects the previous analysis of multidomiance in bi-comparatives in which the degree phrase comprised of the comparative morpheme and the gradable adjective may be shared by the standard when the comparative morpheme is covert. This syntactic analysis proposed in this study will therefore offer a different perspective of how to treat degree phrase in Chinese comparatives and may offer evidence to argue whether there is degree phrase movement in bi-comparatives as in its English counterparts.

Keywords: Chinese comparatives, degree phrase, movement, multidominance, syntactic analysis

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Haohao Wang

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Technology, multimedia in Open Educational Resources, can contribute positively to student performance in an online instructional environment. Student performance data of past four years were obtained from an online course entitled Applied Calculus (MA139). This paper examined the data to determine whether multimedia (independent variable) had any impact on student performance (dependent variable) in online math learning, and how students felt about the value of the technology. Two groups of student data were analyzed, group 1 (control) from the online applied calculus course that did not use multimedia instructional materials, and group 2 (treatment) of the same online applied calculus course that used multimedia instructional materials. For the MA139 class, results indicate a statistically significant difference (p = .001) between the two groups, where group 1 had a final score mean of 56.36 (out of 100), group 2 of 70.68. Additionally, student testimonials were discussed in which students shared their experience in learning applied calculus online with multimedia instructional materials.

Keywords: online learning, open educational resources, multimedia, technology

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Authors: Luis Miguel Méndez Díaz

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In this article, a mathematics teaching-learning strategy will be presented, specifically differential calculus in one variable, in a fun and competitive space in which the action on the part of the student is manifested and not only the repetition of information on the part of the teacher. Said action refers to motivating, problematizing, summarizing, and coordinating a game of dominoes whose thematic cards are designed around the basic and main contents of differential calculus. The strategies for teaching this area are diverse and precisely the game of dominoes is one of the most used strategies in the practice of mathematics because it stimulates logical reasoning and mental abilities. The objective on this investigation is to identify the way in which the game of dominoes affects the learning and understanding of fundamentals concepts of differential calculus in one variable through experimentation carried out on students of the first semester of the School of Engineering and Sciences of the Technological Institute of Monterrey Campus Querétaro. Finally, the results of this study will be presented and the use of this strategy in other topics around mathematics will be recommended to facilitate logical and meaningful learning in students.

Keywords: collaborative learning, logical-mathematical intelligence, mathematical games, multiple intelligences

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Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

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Authors: Anchana Julsiri, Seree Chadcham

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The present study determined the effects of listening to pleasant Thai classical music on increasing working memory in elderly. Thai classical music without lyrics that made participants feel fun and aroused was used in the experiment for 3.19-5.40 minutes. The accuracy scores of Counting Span Task (CST), upper alpha ERD%, and theta ERS% were used to assess working memory of participants both before and after listening to pleasant Thai classical music. The results showed that the accuracy scores of CST and upper alpha ERD% in the frontal area of participants after listening to Thai classical music were significantly higher than before listening to Thai classical music (p < .05). Theta ERS% in the fronto-parietal network of participants after listening to Thai classical music was significantly lower than before listening to Thai classical music (p < .05).

Keywords: brain wave, elderly, pleasant Thai classical music, working memory

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Authors: C. Patrascioiu, V. Matei, N. Nicolae

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The paper describes the experiments and the kinetic parameters calculus of the gasoil hydrofining. They are presented experimental results of gasoil hidrofining using Mo and promoted with Ni on aluminum support catalyst. The authors have adapted a kinetic model gasoil hydrofining. Using this proposed kinetic model and the experimental data they have calculated the parameters of the model. The numerical calculus is based on minimizing the difference between the experimental sulf concentration and kinetic model estimation.

Keywords: hydrofining, kinetic, modeling, optimization

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Authors: Sudhir Kumar Tewatia, Kanishck Tewatia, Anttriksh Tewatia

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Advancements in soil consolidation are discussed, and further improvements are proposed with particular reference to Tewatia’s Y-Y’ Approach, which is called the Settlement versus Rate of Settlement Approach in consolidation. A branch of calculus named Y-Y' (or y versus dy/dx) is suggested (as compared to the common X-Y', x versus dy/dx, dy/dx versus x or Newton-Leibniz branch) that solves some complicated/unsolved theoretical and practical problems in physical sciences (Physics, Chemistry, Mathematics, Biology, and allied sciences) and engineering in an amazingly simple and short manner, particularly when independent variable X is unknown and X-Y' Approach can’t be used. Complicated theoretical and practical problems in 1D, 2D, 3D Primary and Secondary consolidations with non-uniform gradual loading and irregularly shaped clays are solved with elementary school level Y-Y' Approach, and it is interesting to note that in X-Y' Approach, equations become more difficult while we move from one to three dimensions, but in Y-Y' Approach even 2D/3D equations are very simple to derive, solve, and use; rather easier sometimes. This branch of calculus will have a far-reaching impact on understanding and solving the problems in different fields of physical sciences and engineering that were hitherto unsolved or difficult to be solved by normal calculus/numerical/computer methods. Some particular cases from soil consolidation that basically creeps and diffusion equations in isolation and in combination with each other are taken for comparison with heat transfer. The Y-Y’ Approach can similarly be applied in wave equations and other fields wherever normal calculus works or fails. Soil mechanics uses mathematical analogies from other fields of physical sciences and engineering to solve theoretical and practical problems; for example, consolidation theory is a replica of the heat equation from thermodynamics with the addition of the effective stress principle. An attempt is made to give them mathematical analogies.

Keywords: calculus, clay, consolidation, creep, diffusion, heat, settlement

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Authors: Mikhail Bouniaev

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The paper reviews design and implementation of a Calculus Course required for the Biomedical Competency Based Program developed as a joint project between The University of Texas Rio Grande Valley, and the University of Texas’ Institute for Transformational Learning, from the theoretical perspective as presented in scholarly work on active learning, formative assessment, and on-line teaching. Following a four stage curriculum development process (objective, content, delivery, and assessment), and theoretical recommendations that guarantee effectiveness and efficiency of assessment in active learning, we discuss the practical recommendations on how to incorporate a strong formative assessment component to address disciplines’ needs, and students’ major needs. In design and implementation of this project, we used Constructivism and Stage-by-Stage Development of Mental Actions Theory recommendations.

Keywords: active learning, assessment, calculus, cognitive demand, mathematics, stage-by-stage development of mental action theory

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Authors: Truong Nguyen Luan Vu, Le Hieu Giang, Le Linh

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The fractional–order proportional integral (FOPI) controller tuning rules based on the fractional calculus for the cascade control system are systematically proposed in this paper. Accordingly, the ideal controller is obtained by using internal model control (IMC) approach for both the inner and outer loops, which gives the desired closed-loop responses. On the basis of the fractional calculus, the analytical tuning rules of FOPI controller for the inner loop can be established in the frequency domain. Besides, the outer loop is tuned by using any integer PI/PID controller tuning rules in the literature. The simulation study is considered for the stable process model and the results demonstrate the simplicity, flexibility, and effectiveness of the proposed method for the cascade control system in compared with the other methods.

Keywords: Bode’s ideal transfer function, fractional calculus, fractional–order proportional integral (FOPI) controller, cascade control system

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Authors: Rawhy Ismail

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Applying fractional calculus in the field of electromagnetics shows significant results. The fractionalization of the conventional curl operator leads to having additional solutions to an electromagnetic problem. This work restudies the concept of the fractional curl operator considering fractional time derivatives in Maxwell’s curl equations. In that sense, a general scheme for the wave loss term is introduced and the degree of freedom of the system is affected through imposing the new fractional parameters. The conventional case is recovered by setting all fractional derivatives to unity.

Keywords: curl operator, fractional calculus, fractional curl operators, Maxwell equations

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Authors: Sorayya Malek, Mogeeb Mosleh, Sharifah M. Syed

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In this study, Support Vector Machine (SVM) technique was applied to predict the dichotomized value of Dissolved oxygen (DO) from two freshwater lakes namely Chini and Bera Lake (Malaysia). Data sample contained 11 parameters for water quality features from year 2005 until 2009. All data parameters were used to predicate the dissolved oxygen concentration which was dichotomized into 3 different levels (High, Medium, and Low). The input parameters were ranked, and forward selection method was applied to determine the optimum parameters that yield the lowest errors, and highest accuracy. Initial results showed that pH, water temperature, and conductivity are the most important parameters that significantly affect the predication of DO. Then, SVM model was applied using the Anova kernel with those parameters yielded 74% accuracy rate. We concluded that using SVM models to predicate the DO is feasible, and using dichotomized value of DO yields higher prediction accuracy than using precise DO value.

Keywords: dissolved oxygen, water quality, predication DO, support vector machine

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Authors: Rui-heng Ray Huang

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This study compares the syntax and semantics of two kinds of passives in Mandarin Chinese: bèi passives and yóu passives. To express a Chinese equivalent for ‘The thief was taken away by the police,’ either bèi or yóu can be used, as in Xiǎotōu bèi/yóu jǐngchá dàizǒu le. It is shown in this study that bèi passives and yóu passives differ semantically and syntactically. The semantic observations are based on the theta theory, dealing with thematic roles. On the other hand, the syntactic analysis draws heavily upon the generative grammar, looking into thematic structures. The findings of this study are as follows. First, the core semantics of bèi passives is centered on the Patient NP in the subject position. This Patient NP is essentially an Affectee, undergoing the outcome or consequence brought up by the action represented by the predicate. This may explain why in the sentence Wǒde huà bèi/*yóu tā niǔqū le ‘My words have been twisted by him/her,’ only bèi is allowed. This is because the subject NP wǒde huà ‘my words’ suffers a negative consequence. Yóu passives, in contrast, place the semantic focus on the post-yóu NP, which is not an Affectee though. Instead, it plays a role which has to take certain responsibility without being affected in a way like an Affectee. For example, in the sentence Zhèbù diànyǐng yóu/*bèi tā dānrèn dǎoyǎn ‘This film is directed by him/her,’ only the use of yóu is possible because the post-yóu NP tā ‘s/he’ refers to someone in charge, who is not an Affectee, nor is the sentence-initial NP zhèbù diànyǐng ‘this film’. When it comes to the second finding, the syntactic structures of bèi passives and yóu passives differ in that the former involve a two-place predicate while the latter a three-place predicate. The passive morpheme bèi in a case like Xiǎotōu bèi jǐngchá dàizǒu le ‘The thief was taken away by the police’ has been argued by some Chinese syntacticians to be a two-place predicate which selects an Experiencer subject and an Event complement. Under this analysis, the initial NP xiǎotōu ‘the thief’ in the above example is a base-generated subject. This study, however, proposes that yóu passives fall into a three-place unergative structure. In the sentence Xiǎotōu yóu jǐngchá dàizǒu le ‘The thief was taken away by the police,’ the initial NP xiǎotōu ‘the thief’ is a topic which serves as a Patient taken by the verb dàizǒu ‘take away.’ The subject of the sentence is assumed to be an Agent, which is in a null form and may find its reference from the discourse or world knowledge. Regarding the post-yóu NP jǐngchá ‘the police,’ its status is dual. On the one hand, it is a Patient introduced by the light verb yóu; on the other, it is an Agent assigned by the verb dàizǒu ‘take away.’ It is concluded that the findings in this study contribute to better understanding of what makes the distinction between the two kinds of Chinese passives.

Keywords: affectee, passive, patient, unergative

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Authors: Nodelman V.

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Despite serious difficulties in the assimilation of the conceptual system of Calculus, software in the educational process is used only occasionally, and even then, mainly for illustration purposes. The following are a few reasons: The non-trivial nature of the studied material, Lack of skills in working with software, Fear of losing time working with software, The variety of the software itself, the corresponding interface, syntax, and the methods of working with the software, The need to find suitable models, and familiarize yourself with working with them, Incomplete compatibility of the found models with the content and teaching methods of the studied material. This paper proposes an active use of the developed non-commercial software VusuMatica, which allows removing these restrictions through Broad support for the studied mathematical material (and not only Calculus). As a result - no need to select the right software, Emphasizing the unity of mathematics, its intrasubject and interdisciplinary relations, User-friendly interface, Absence of special syntax in defining mathematical objects, Ease of building models of the studied material and manipulating them, Unlimited flexibility of models thanks to the ability to redefine objects, which allows exploring objects characteristics, and considering examples and counterexamples of the concepts under study. The construction of models is based on an original approach to the analysis of the structure of the studied concepts. Thanks to the ease of construction, students are able not only to use ready-made models but also to create them on their own and explore the material studied with their help. The presentation includes examples of using VusuMatica in studying the concepts of limit and continuity of a function, its derivative, and integral.

Keywords: counterexamples, limitations and requirements, software, teaching and learning calculus, user-friendly interface and syntax

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Authors: Golden J. Zhang, Dongbao Zhou

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Darcy’s law is the fundamental theory in fluid dynamics and engineering applications. Although Darcy linearity was found to be valid for slow, viscous flow, non-linear and non-Darcian flow has been well documented under both small and large velocity fluid flow. Various classical models were proposed and used widely to quantify non-Darcian flow, including the well-known Forchheimer, Izbash, and Swartzendruber models. Applications, however, revealed limitations of these models. Here we propose a general model built upon the Caputo fractional derivative to quantify non-Darcian flow for various flows (laminar to turbulence).Real-world applications and model comparisons showed that the new fractional-derivative model, which extends the fractional model proposed recently by Zhou and Yang (2018), can capture the non-Darcian flow in the relatively small velocity in low-permeability deposits and the relatively high velocity in high-permeability sand. A scale effect was also identified for non-Darcian flow in fractured rocks. Therefore, fractional calculus may provide an efficient tool to improve classical models to quantify fluid dynamics in aquatic environments.

Keywords: fractional derivative, darcy’s law, non-darcian flow, fluid dynamics

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Authors: Yusuf Seller

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Classical Arabic poetry was narrated by the followers of poets, who were memorizing and repeating all the couplets of their master constantly. Although the students established their own styles, it was very natural for them to reflect the style and expression of their masters. This reflection was discussed in classical Arabic literary criticism and rhetoric (al-‘ilm al-balagha), as “al-Sariqah al-shiriyyah”, plagiarism in poetry. This study tests the claim that the reflection of the master's style and expressions in the student's poetry cannot be considered plagiarism. In addition, one of the goals of this essay is also to investigate the methodological emergence of plagiarism phenomena in classical Arabic poetry. The investigation of the methodological origins of plagiarism helps us see the relationship of plagiarism with literary property and the extent of the property`s authenticity. Therefore, the focus is directed towards uncovering the underlying ethical principles governing literary works and academic research in classical Arabic poetry.

Keywords: Arabic literary criticism, classical Arabic poetry, plagiarism, al-Sariqah al-shiriyyah

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Authors: Carine Kawakami

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In French, as well as in English, there are two types of psychological predicate constructions depending on where the experiencer argument is realized; the first type is in the subject position (e.g. Je regrette d’être venu ici. ‘I regret coming here'), hereinafter called ES construction, and the second type is in the object position (e.g. Cette nouvelle m’a surpris. ‘This new surprised me.'), referred as EO construction. In the previous studies about psychological predicates, the syntactic position of the experiencer argument has been just a matter of its connection with the syntactic or semantic structure of the predicate. So that few attentions have been paid to how two types of realization of experiencer are related to the conceptualization of psychological event and to the function of the sentence describing the psychological event, in the sense of speech act theory. In this research, focusing on the French phenomena limited to the first personal pronoun and the present tense, the ES constructions and the EO constructions will be analyzed from cognitive and functional approach. It will be revealed that, due to the possibility to be used in soliloquy and the high co-occurrence with ça (‘it’), the EO constructions may have expressive function to betray what speaker feels in hic et nunc, like interjection. And in the expressive case, the experiencer is construed as a locus where a feeling appears spontaneously and is construed subjectively (e.g. Ah, ça m’énerve! ‘Oh, it irritates me!'). On the other hand, the ES constructions describe speaker’s mental state in an assertive manner rather than the expressive and spontaneously way. In other words, they describe what speaker feels to the interlocutor (e.g. Je suis énervé. ‘I am irritated.'). As a consequence, when the experiencer argument is realized in the subject position, it is construed objectively and have a participant feature in the sense of cognitive grammar. Finally, it will be concluded that the choice of construction type, at least in French, is correlated to the conceptualization of the psychological event and the discourse feature of its expression.

Keywords: french psychological verb, conceptualization, expressive function, assertive function, experiencer realization

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Authors: Ayan Chakraborty, BV. Rathish Kumar

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Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in the different field of science have been reconsidered in this term like diffusion wave equations, Schr$\ddot{o}$dinger equation and so on. In the present paper, a time-dependent tempered fractional diffusion equation of order $\gamma \in (0,1)$ with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank-Nicolson discretization is used in the time direction. B spline finite element approximation is implemented. Generally, B-splines basis are useful for representing the geometry of a finite element model, interfacing a finite element analysis program. By utilizing this technique a priori space-time estimate in finite element analysis has been derived and we proved that the convergent order is $\mathcal{O}(h²+T²)$ where $h$ is the space step size and $T$ is the time. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.

Keywords: B-spline finite element, error estimates, Gronwall's lemma, stability, tempered fractional

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Authors: Orit Wolf

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Classical music confronts a crucial challenge: updating cherished concert traditions for the digital age. This paper is a journey, and a quest to make classical concerts resonate with a new generation. It's not just about asking questions; it's about exploring the future of classical concerts and their potential to captivate and connect with today's audience in an era defined by change. The younger generation, known for their love of diversity, interactive experiences, and multi-sensory immersion, cannot be overlooked. This paper explores innovative strategies that forge deep connections with audiences whose relationship with classical music differs from the past. The urgency of this challenge drives the transformation of classical concerts. Examining classical concerts is necessary to understand how they can harmonize with contemporary sensibilities. New dimensions in audiovisual experiences that enchant the emerging generation are sought. Classical music must embrace the technological era while staying open to fusion and cross-cultural collaboration possibilities. The role of technology and Artificial Intelligence (AI) in reshaping classical concerts is under research. The fusion of classical music with digital experiences and dynamic interdisciplinary collaborations breathes new life into the concert experience. It aligns classical music with the expectations of modern audiences, making it more relevant and engaging. Exploration extends to the structure of classical concerts. Conventions are challenged, and ways to make classical concerts more accessible and captivating are sought. Inspired by innovative artistic collaborations, musical genres and styles are redefined, transforming the relationship between performers and the audience. This paper, therefore, aims to be a catalyst for dialogue and a beacon of innovation. A set of critical inquiries integral to reshaping classical concerts for the digital age is presented. As the world embraces digital transformation, classical music seeks resonance with contemporary audiences, redefining the concert experience while remaining true to its roots and embracing revolutions in the digital age.

Keywords: new concert formats, reception of classical music, interdiscplinary concerts, innovation in the new musical era, mash-up, cross culture, innovative concerts, engaging musical performances

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Authors: Hukam Chand

Abstract:

Over the past few years, the performance of Indian classical music has been improved a lot due to the technical inclusion of western instruments. Infect, the Indian classical music is all about raags which portray a mood and sentiments expressed through a microtonal scale based on natural harmonic series. And, most of the western instruments are not based on natural harmonic series and the tonal system is the only system which has considerable influence on the Indian classical music. However, the use of western instruments has been growing day by day in one way or the other by the Indian artists due to their quality of harmony. As a result of which, there are some common instruments such as harmonium, violin, guitar, saxophone, synthesizer which are being used commonly by Indian and western artists. On the other hand, a lot of fusion has taken place in the music of both sides due to the similar characteristics in their instruments. For example, harmonium which was originally the western instrument has now acquired an important position in Indian classical music to perform raags. Besides, a lot of suggestions for improving in the Indian music have been given by the artists for technical modification in the western instruments to cater the needs of Indian music through melody approach. Pt. Vishav Mohan Bhatt an Indian musician has developed Mohan Veena (called guitar) to perform raags. N. Rajam the Indian lady Violinist has made a remarkable work on Indian classical music by accompanied with vocal music. The purpose of the present research paper is to highlight the changes in Indian Classical Music through performance by using modified western music instruments.

Keywords: Indian classical music, Western instruments, harmonium, guitar, Violin and impact

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Authors: M. O. Adda

Abstract:

In this paper, we propose a topology called Zoned fat tree (Z-Fat tree) which is a further extension to the classical fat trees. The extension relates to the provision of extra degree of connectivity to maximize the number of deployed ports per routing nodes, and hence increases the bisection bandwidth especially for slimmed fat trees. The extra links, when classical routing is used, tend, in deterministic environment, to be under-utilized for some traffic patterns, hence achieving poor performance. We suggest two versions of a dynamic round robin scheme that outperforms the classical D-mod-k and S-mod-K routing and show by simulation that our proposal utilize all the extra added links to the classical fat tree, and achieve better performance for general applications.

Keywords: deterministic routing, fat tree, interconnection, traffic pattern

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Authors: Barenten Suciu

Abstract:

In this paper, effectiveness of a machine design process is evaluated on the basis of the specific output calculus. Concretely, a screw-worm gear mechanical transmission is designed by using the classical and the 3D-CAD methods. Strength analysis and drawing of the designed parts is substantially aided by employing the SolidWorks software. Quality of the design process is assessed by manufacturing (printing) the parts, and by computing the efficiency, specific load, as well as the specific output (work) of the mechanical transmission. Influence of the stroke, travelling velocity and load on the mechanical output, is emphasized. Optimal design of the mechanical transmission becomes possible by the appropriate usage of the acquired results.

Keywords: mechanical transmission, design, screw, worm-gear, efficiency, specific output, 3D-printing

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Authors: Jerome Joshi

Abstract:

The paper presents the modelling of financial markets using the Stochastic Pi Calculus model. The Stochastic Pi Calculus model is mainly used for biological applications; however, the feature of this model promotes its use in financial markets, more prominently in high frequency trading. The trading system can be broadly classified into exchange, market makers or intermediary traders and fundamental traders. The exchange is where the action of the trade is executed, and the two types of traders act as market participants in the exchange. High frequency trading, with its complex networks and numerous market participants (intermediary and fundamental traders) poses a difficulty while modelling. It involves the participants to seek the advantage of complex trading algorithms and high execution speeds to carry out large volumes of trades. To earn profits from each trade, the trader must be at the top of the order book quite frequently by executing or processing multiple trades simultaneously. This would require highly automated systems as well as the right sentiment to outperform other traders. However, always being at the top of the book is also not best for the trader, since it was the reason for the outbreak of the ‘Hot – Potato Effect,’ which in turn demands for a better and more efficient model. The characteristics of the model should be such that it should be flexible and have diverse applications. Therefore, a model which has its application in a similar field characterized by such difficulty should be chosen. It should also be flexible in its simulation so that it can be further extended and adapted for future research as well as be equipped with certain tools so that it can be perfectly used in the field of finance. In this case, the Stochastic Pi Calculus model seems to be an ideal fit for financial applications, owing to its expertise in the field of biology. It is an extension of the original Pi Calculus model and acts as a solution and an alternative to the previously flawed algorithm, provided the application of this model is further extended. This model would focus on solving the problem which led to the ‘Flash Crash’ which is the ‘Hot –Potato Effect.’ The model consists of small sub-systems, which can be integrated to form a large system. It is designed in way such that the behavior of ‘noise traders’ is considered as a random process or noise in the system. While modelling, to get a better understanding of the problem, a broader picture is taken into consideration with the trader, the system, and the market participants. The paper goes on to explain trading in exchanges, types of traders, high frequency trading, ‘Flash Crash,’ ‘Hot-Potato Effect,’ evaluation of orders and time delay in further detail. For the future, there is a need to focus on the calibration of the module so that they would interact perfectly with other modules. This model, with its application extended, would provide a basis for researchers for further research in the field of finance and computing.

Keywords: concurrent computing, high frequency trading, financial markets, stochastic pi calculus

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