Готові списки джерел за темами / Fractional notations

Добірка наукової літератури з теми "Fractional notations"

Автор: Grafiati

Опубліковано: 12 червня 2021

Оновлено: 2 лютого 2022

Оформте джерело за APA, MLA, Chicago, Harvard та іншими стилями

Оберіть тип джерела:

Ознайомтеся зі списками актуальних статей, книг, дисертацій, тез та інших наукових джерел на тему "Fractional notations".

Біля кожної праці в переліку літератури доступна кнопка «Додати до бібліографії». Скористайтеся нею – і ми автоматично оформимо бібліографічне посилання на обрану працю в потрібному вам стилі цитування: APA, MLA, «Гарвард», «Чикаго», «Ванкувер» тощо.

Також ви можете завантажити повний текст наукової публікації у форматі «.pdf» та прочитати онлайн анотацію до роботи, якщо відповідні параметри наявні в метаданих.

Статті в журналах з теми "Fractional notations":

Abd El-Salam, F. A. "-Dimensional Fractional Lagrange's Inversion Theorem." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/310679.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

Alzabut, Jehad, Velu Muthulakshmi, Abdullah Özbekler, and Hakan Adıgüzel. "On the Oscillation of Non-Linear Fractional Difference Equations with Damping." Mathematics 7, no. 8 (August 1, 2019): 687. http://dx.doi.org/10.3390/math7080687.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

In studying the Riccati transformation technique, some mathematical inequalities and comparison results, we establish new oscillation criteria for a non-linear fractional difference equation with damping term. Preliminary details including notations, definitions and essential lemmas on discrete fractional calculus are furnished before proceeding to the main results. The consistency of the proposed results is demonstrated by presenting some numerical examples. We end the paper with a concluding remark.

Ibnelazyz, Lahcen, Karim Guida, Said Melliani, and Khalid Hilal. "On a Nonlocal Multipoint and Integral Boundary Value Problem of Nonlinear Fractional Integrodifferential Equations." Journal of Function Spaces 2020 (October 28, 2020): 1–8. http://dx.doi.org/10.1155/2020/8891736.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

The aim of this paper is to give the existence as well as the uniqueness results for a multipoint nonlocal integral boundary value problem of nonlinear sequential fractional integrodifferential equations. First of all, we give some preliminaries and notations that are necessary for the understanding of the manuscript; second of all, we show the existence and uniqueness of the solution by means of the fixed point theory, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Last, but not least, we give two examples to illustrate the results.

Sikora, Ryszard, and Stanislaw Pawłowski. "Fractional derivatives and the laws of electrical engineering." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 4 (July 2, 2018): 1384–91. http://dx.doi.org/10.1108/compel-08-2017-0347.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

Purpose This paper aims to evaluate the possibilities of fractional calculus application in electrical circuits and magnetic field theories. Design/methodology/approach The analysis of mathematical notation is used for physical phenomena description. The analysis aims to challenge or prove the correctness of applied notation. Findings Fractional calculus is sometimes applied correctly and sometimes erroneously in electrical engineering. Originality/value This paper provides guidelines regarding correct application of fractional calculus in description of electrical circuits’ phenomena. It can also inspire researchers to find new applications for fractional calculus in the future.

Yüce, Ali, Nusret Tan, and Derek P. Atherton. "Limit cycles in relay systems with fractional order plants." Transactions of the Institute of Measurement and Control 41, no. 15 (July 4, 2019): 4424–35. http://dx.doi.org/10.1177/0142331219860302.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

In this paper, limit cycle frequency, pulse width and stability analysis are examined using different methods for relay feedback nonlinear control systems with integer or fractional order plant transfer functions. The describing function (DF), A loci, a time domain method formulated in state space notation and Matlab/Simulink simulations are used for the analysis. Comparisons of the results of using these methods are given in several examples. In addition, the work has been extended to fractional order systems with time delay. Programs have been developed in the Matlab environment for all the theoretical methods. In particular, Matlab programs have been written to obtain a graphical solution for the A loci method, which can precisely calculate the limit cycle frequency. The developed solution methods are shown in various examples. The major contribution is to look at finding limit cycles for relay feedback systems having plants with a fractional order transfer function (FOTF). However, en route to this goal new assessments of limit cycle stability have been done for a rational plant transfer function plus a time delay.

Rios-Avila, Fernando. "Estimation of marginal effects for models with alternative variable transformations." Stata Journal: Promoting communications on statistics and Stata 21, no. 1 (March 2021): 81–96. http://dx.doi.org/10.1177/1536867x211000005.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

margins is a powerful postestimation command that allows the estimation of marginal effects for official and community-contributed commands, with well-defined predicted outcomes (see predict). While the use of factor-variable notation allows one to easily estimate marginal effects when interactions and polynomials are used, estimation of marginal effects when other types of transformations such as splines, logs, or fractional polynomials are used remains a challenge. In this article, I describe how margins‘s capabilities can be extended to analyze other variable transformations using the command f_able.

Mohammed, Pshtiwan Othman, Mehmet Zeki Sarikaya, and Dumitru Baleanu. "On the Generalized Hermite–Hadamard Inequalities via the Tempered Fractional Integrals." Symmetry 12, no. 4 (April 8, 2020): 595. http://dx.doi.org/10.3390/sym12040595.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a concrete role in the field of inequalities due to the behaviour of its definition. There is a strong relationship between convexity and symmetry. Which ever one we work on, we can apply to the other one due to the strong correlation produced between them especially in recent few years. In this article, we first introduced the notion of λ -incomplete gamma function. Using the new notation, we established a few inequalities of the Hermite–Hadamard (HH) type involved the tempered fractional integrals for the convex functions which cover the previously published result such as Riemann integrals, Riemann–Liouville fractional integrals. Finally, three example are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.

Boyd, Clifton. "Metrical Ambiguity in the Scherzo of Brahms's String Sextet, Op. 18." Music Theory and Analysis (MTA) 8, no. 1 (April 30, 2021): 41–60. http://dx.doi.org/10.11116/mta.8.1.2.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

This article explores the metrical and hypermetrical ambiguities present in the Scherzo of Brahms's String Sextet in B♭ major, Op. 18 (1859–60). Drawing upon Lerdahl and Jackendoff's metrical preference rules, Mirka's parallel multiple-analysis model, and Ito's fractional notation, I argue that each hearing of material from the opening phrase (at the beginning, during its first repeat, after the Trio, etc.) affords the possibility of a different hypermetrical experience. Furthermore, rather than the metrical structure becoming increasingly clear over time, there are a number of hypermetrical irregularities that can lead listeners to question their previous interpretations. The article concludes with suggestions on how chamber ensembles can utilize metrical analyses of this movement to inform their performances and create varied listening experiences.

Oppenheimer, Lauren, and Robert P. Hunting. "Reflections on Practice: Relating Fractions and Decimals: Listening to Students Talk." Mathematics Teaching in the Middle School 4, no. 5 (February 1999): 318–21. http://dx.doi.org/10.5951/mtms.4.5.0318.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

Despite the great amount of time that middle-grades teachers devote to teaching fractions and decimals, converting between these two representations continues to be a difficult task for students. According to the results of the sixth National Assessment of Educational Progress (NAEP) conducted in 1992, although 90 percent of eighth-grade students correctly paired a simple fraction with its pictorial representation, only 63 percent of students successfully shaded a fractional portion of a given rectangular region using equivalent fractions. Likewise, 92 percent correctly identified 14.9 seconds as being the decimal representation closest to 15 seconds, but when comparing common fractions with decimal notation, only 51 percent of eighth-grade students chose 1/2 as being the fraction closest to 0.52. Twenty-nine percent of eighth graders chose the fraction 1/50 as being closest in value to 0.52 (Kouba, Zawojewski, and Struchens 1997).

Shishkina, E. L. "General Euler-Poisson-Darboux Equation and Hyperbolic B-Potentials." Contemporary Mathematics. Fundamental Directions 65, no. 2 (December 15, 2019): 157–338. http://dx.doi.org/10.22363/2413-3639-2019-65-2-157-338.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

In this work, we develop the theory of hyperbolic equations with Bessel operators. We construct and invert hyperbolic potentials generated by multidimensional generalized translation. Chapter 1 contains necessary notation, deﬁnitions, auxiliary facts and results. In Chapter 2, we study some generalized weight functions related to a quadratic form. These functions are used below to construct fractional powers of hyperbolic operators and solutions of hyperbolic equations with Bessel operators. Chapter 3 is devoted to hyperbolic potentials generated by multidimensional generalized translation. These potentials express negative real powers of the singular wave operator, i. e. the wave operator where the Bessel operator acts instead of second derivatives. The boundedness of such an operator and its properties are investigated and the inverse operator is constructed. The hyperbolic Riesz B-potential is studied as well in this chapter. In Chapter 4, we consider various methods of solution of the Euler-Poisson-Darboux equation. We obtain solutions of the Cauchy problems for homogeneous and nonhomogeneous equations of this type. In Conclusion, we discuss general methods of solution for problems with arbitrary singular operators.

Більше джерел

Дисертації з теми "Fractional notations":

Ngola-Kazumba, Maria. "An investigation on how learners may use multiple representations in a social interaction to promote learning of percentages and fractions: a case study." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1006057.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

The study examined the use of multiple representations such as the real world, written symbols, spoken symbols, diagrams and manipulatives by learners to promote the learning of percentages and fractions through social interaction. This investigation was carried out through a teaching and learning programme which was developed and implemented by me, the researcher. The effect of the implemented programme was the main focus of the research. The qualitative study was oriented in the interpretive paradigm – a paradigm that seeks to understand the meaning attached to human actions. Twenty learners participated in the implementation of the programme and 9 learners were selected for focus group interviews. The purpose of the interviews was to explore learners' understanding and feelings about the use of multiple representations in the learning of percentages and fractions through social interactions. The other tools employed in this study were pre-and-post diagnostic tests, observations, learners' work and a journal. The pre-test was used to determine learners' prior knowledge for the program design and implementation, while the post-test and learners' work were used to analyze the effect of the programme. Observations were used to investigate how multiple representations promoted or did not promote the learning of percentages and fractions. The teacher's journal was to record and reflect on any relevant information gathered on each lesson observed. The data shows that the effective use of multiple representations helped learners learn the concept of percentages and fractions better. Learners were able to look at representations in useful ways; multiple representations made some aspects of the concept clear; and multiple representations enabled learners to correct errors. Through the interaction between the teacher and learners, the following was found: all the learners changed words to change focus; learners made links between multiple representations; the learners deepened their concepts of percentages and fractions; learners could convert between fractions using multiple representations; learners could work out percentages of a quantity; and learners could express one quantity as a percentage of another. Furthermore, through the interaction between learners and learners all learners could identify more equivalent fractions of an initial fraction which was given to them; and they could increase and decrease a quantity by a given percentage. On the basis of this research, it can be concluded that the programme promoted the learning of percentages and fractions through three effective methodologies. The first methodology consisted of the effective use of multiple representations; the second methodology concerned the interaction between the teacher and learner during the learning process and the last methodology related to the interaction between the learners - interactions that were not strongly mediated by the teacher. I would recommend that teachers use these three effective approaches when teaching percentages and fractions to promote the learning of the concepts.

Sebaï, Nassira. "Des tâches d’évaluation en mathématiques au livret scolaire : Étude qualitative des pratiques de huit enseignants de CM1 et CM2." Thesis, Paris 5, 2012. http://www.theses.fr/2012PA05H018/document.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

L’approche par les compétences fait partie de la rénovation des systèmes éducatifs. La loi de 1990 institue, pour chaque élève, un livret scolaire qui s’appuie sur des référentiels de compétences. Nous étudions les pratiques d’évaluation et du quotidien de huit professeurs des écoles de CM1 et de CM2. Notre recherche, descriptive, se place dans le cadre des réflexions sur les pratiques enseignantes. Elle se situe dans le champ de la didactique et s’appuie sur des contenus disciplinaires en mathématiques dans deux domaines de connaissance : les fractions et la résolution de problèmes. Notre dispositif d’étude des pratiques enseignantes s’appuie sur un corpus constitué de tâches d’évaluation et de tâches du quotidien ainsi que sur des entretiens à visée compréhensive pendant lesquels les maîtres corrigent les copies de trois à quatre élèves de niveau scolaire moyen choisies par eux. Il s’agit de comprendre le processus d’évaluation depuis le choix des tâches jusqu’au remplissage du livret scolaire qui sert à communiquer sur les acquis des élèves. Nos résultats montrent que l’évaluation des compétences se fait chez l’ensemble des professeurs à travers des tâches standardisées dans le domaine des fractions. Dans la résolution de problèmes, les tâches sont décomposées chez les professeurs qui adhèrent à l’APC alors qu’elles ne le sont pas chez ceux qui ne se préoccupent pas des compétences. Lors de l’évaluation des productions des élèves, les erreurs n’ont pas un statut « formatif ». Les livrets scolaires ont une fonction sommative. Ils fonctionnent comme des bulletins de notes
The competency-based instruction is an integral part of the renewal of education systems. The 1990 law introduces, for each pupil, a report book based on reference frameworks for competences. We study the evaluation practices and the daily professional lives of eight 4th-5th grade teachers. Our research adopts a descriptive approach and comes within the reflections on teaching practices. It belongs to the field of didactics and employs subject-specific contents in two knowledge fields of mathematics, i.e. the fractions and problem solving. Our study scheme for teaching practices lies on a corpus of evaluation and daily tasks as well as on a set of comprehensive interviews during which the teachers select and grade the exams of three or four pupils with an average school level. The aim is to understand the evaluation process from the choice of tasks to the filling up of report books which serve as communication supports for the pupils’ achievements.The results show that, for all teachers, the evaluation of competences is achieved through a set of standardized tasks in the field of fractions. Regarding the problem solving field teachers supporting the APC break down the tasks while teachers, that are less concerned about the competences, do not proceed in the same manner. During the pupils’ evaluation, the mistakes do not have any formative function. The report books carry out a summative function. They are assimilated to grades reports

Moloto, Phuti Margaeret. "An exploration of mathematical knowledge for teaching for Grade 6 teachers in the teaching of fractions : a case study of three schools in Capricorn South District." Diss., 2020. http://hdl.handle.net/10500/27361.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

The study aimed to explore teachers’ mathematical knowledge in respect of teaching the concept of fractions to Grade 6 learners. To that end a qualitative study was done, using a case study design. Data were collected through the observation of, and interviews with, three teachers at three schools in the Capricorn South district. Rooted in the theory of constructivism, the study was supplemented by the conceptual framework of mathematical knowledge for teaching (MKT) (Ball et al., 2008) and Shulman’s (1986) notion of pedagogical knowledge for teaching (PCK). The key finding of this investigation revealed that, of the three teachers, two did not develop the concept of fractions for their learners, but merely followed the traditional method of teaching the concept by encouraging their learners to memorise rules without understanding. Only one teacher emphasised an understanding of mathematical concepts. The main observation which the researcher made, was that teachers require a great deal of knowledge and expertise, in carrying out the work of teaching subject matter related to fractions.
Mathematics Education

Книги з теми "Fractional notations":

Music Math: Exploring Different Interpretations of Fractions (Powermath). PowerKids Press, 2004.

Знайти повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Collins, Kathleen. Music Math: Exploring Different Interpretations of Fractions (Powermath). PowerKids Press, 2004.

Знайти повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Globe Fearon. Access to Math: Exponents & Scientific Notation (Access to Math). Globe Fearon, 1996.

Знайти повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Globe Fearon. Access to Math: Exponents and Scientific Notation (Access to Math). Globe Fearon, 1996.

Знайти повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Tzelgov, Joseph, Dana Ganor-Stern, Arava Kallai, and Michal Pinhas. Primitives and Non-primitives of Numerical Representations. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.019.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

Primitives of numerical representation are numbers holistically represented on the mental number line (MNL). Non-primitives are numbers generated from primitives in order to perform specific tasks. Primitives can be automatically retrieved from long-term memory (LTM). Using the size congruency effect in physical comparisons as a marker of automatic retrieval, and its modulation by intrapair numerical distance as an indication of alignment along the MNL, we identify single-digits, but not two-digit numbers, as primitives. By the same criteria, zero is a primitive, but negative numbers are not primitives, which makes zero the smallest numerical primitive. Due to their unique notational structure, fractions are automatically perceived as smaller than 1. While some specific, familiar unit fractions may be primitives, this can be shown only when component bias is eliminated by training participants to denote fractions by unfamiliar figures.

Stroud, Barry. Concepts of Colour and Limits of Understanding. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198809753.003.0016.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

This chapter examines some puzzling reflections by Ludwig Wittgenstein on the possibility of understanding concepts of the colours of things different from those already familiar to us. It begins with a discussion of Wittgenstein’s statement: ‘Someone who has perfect pitch can learn a language-game that I cannot learn’. In particular, it considers how Wittgenstein draws a connection between perfect pitch and concepts of colours and invites us to imagine people who speak of colours intermediate between red and yellow by means of fractions in a kind of binary notation representing different proportions of the colours at each end of the range from red to yellow. The chapter also analyses Wittgenstein’s views on whether the number system and the colour system ‘reside in our nature or in the nature of things’.

Частини книг з теми "Fractional notations":

"Notations." In The Theory of Fractional Powers of Operators, 341–46. Elsevier, 2000. http://dx.doi.org/10.1016/s0304-0208(00)80039-0.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Imhausen, Annette. "Notation of Fractions." In Mathematics in Ancient Egypt. Princeton University Press, 2016. http://dx.doi.org/10.23943/princeton/9780691117133.003.0008.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

This chapter discusses the development of the ancient Egyptian concept of fractions. The beginnings of fractions in ancient Egypt consisted of a small group of specific fractions written by special signs. These fractions are first attested within the context of metrological systems, but they retain their notation in later times as abstract fractions. The list of earliest fractions comprises 1/2, 1/3, and 1/4, and it may be inferred that fractions came to be understood as the inverses of integers. As a consequence, the Egyptian notation of fractions did not consist of numerator and denominator but rather of the respective integer of which the fraction was the inverse and a symbol to designate it as an inverse, that is, a fraction. Following the concept of fractions as inverses of integers, the next step would have been to express parts that consist of more than one of these inverses. This was done by (additive) juxtaposition of different inverses.

"From Leibniz’s Notation for Derivative to the Fractal Derivative, Fractional Derivative and Application in Mongolian Yurt." In Fractional Dynamics, 219–30. De Gruyter Open Poland, 2015. http://dx.doi.org/10.1515/9783110472097-013.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

"7. Notation of Fractions." In Mathematics in Ancient Egypt, 52–54. Princeton University Press, 2015. http://dx.doi.org/10.1515/9781400874309-009.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Тези доповідей конференцій з теми "Fractional notations":

Ge, Fudong, YangQuan Chen, and Chunhai Kou. "The Adjoint Systems of Time Fractional Diffusion Equations and Their Applications in Controllability Analysis." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46696.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

This paper is devoted to the construction of the adjoint system for the case of time fractional order diffusion equations. We first obtain the equivalent integral equation of the abstract fractional state-space system of both Caputo and Riemann-Liouville type by utilizing the Laplace transform and the semigroup theory. Then the adjoint system of time fractional diffusion equation is introduced and used to analyze the duality relationship between observation and control in a Hilbert space. The new introduced notations can also be used in many fields of modelling and control of real dynamic systems.

Nakayama, Shin, Keiji Ueda, Masahiro Aoki, and Kazuyuki Matsumoto. "Enhancement of Structural Redundancy of Hull Structure in Accidental Condition by Applying Highly Ductile Steel." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95912.

Повний текст джерела

Стилі APA, Harvard, Vancouver, ISO та ін.

Анотація:

Abstract Application of steel plates with highly ductile is beneficial for ship owners, in order to improve structural redundancy and prevent environmental burden in accidental condition such as collision or grounding. Highly ductile steel, in which breaking strain is improved by 20% in comparison with conventional steels has developed, by optimizing microstructure. Excellent ductility was achieved selecting ferrite-perlite dual phase structure of ferrite phase which is advantageous for stable actual production. Morphology of ferrite phase control which consists of optimization of volume fraction and strengthening of ferrite phase itself by adding Si plays an important role to enhance ductility. The highly ductile steel of YP315 grade had acquired Class approval, and for ships to which high ductile steels are applied, ClassNK would assign the notation “Hull Protection by Highly Ductile Steel” (HP-HDS). MITSUBISHI SHIPBUILDING has evaluated the effect of highly ductile steel by numerical simulation for LPG (Liquefied Petroleum Gas) Carrier owned by Astomos Energy Corporation and Iino Kaiun Kaisha, Ltd. It has been confirmed that highly ductile steel can improve the structural redundancy by 20% in accidental condition by being applying to side structure.