Gotowe bibliografie tematyczne / Operations on rational numbers

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Gotowa bibliografia na temat „Operations on rational numbers”

Autor: Grafiati
Data publikacji: 2 czerwca 2025
Data aktualizacji: 31 lipca 2025

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Artykuły w czasopismach na temat "Operations on rational numbers"

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Christou, Konstantinos P., Courtney Pollack, Jo Van Hoof, and Wim Van Dooren. "Natural number bias in arithmetic operations with missing numbers – A reaction time study." Journal of Numerical Cognition 6, no. 1 (2020): 22–49. http://dx.doi.org/10.5964/jnc.v6i1.228.

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When reasoning about numbers, students are susceptible to a natural number bias (NNB): When reasoning about non-natural numbers they use properties of natural numbers that do not apply. The present study examined the NNB when students are asked to evaluate the validity of algebraic equations involving multiplication and division, with an unknown, a given operand, and a given result; numbers were either small or large natural numbers, or decimal numbers (e.g., 3 × _ = 12, 6 × _ = 498, 6.1 × _ = 17.2). Equations varied on number congruency (unknown operands were either natural or rational number
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Moss, Joan. "Research, Reflection, Practice: Introducing Percents in Linear Measurement to Foster an Understanding of Rational-Number Operations." Teaching Children Mathematics 9, no. 6 (2003): 335–39. http://dx.doi.org/10.5951/tcm.9.6.0335.

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How do we foster computational fluency with rational numbers when this topic is known to pose so many conceptual challenges for young students? How can we help students understand the operations of rational numbers when their grasp of the quantities involved in the rational-number system is often very limited? Traditional instruction in rational numbers focuses on rules and memorization. Teachers often give students instructions such as, “To add fractions, first find a common denominator, then add only the numerators” or “To add and subtract decimal numbers, line up the decimals, then do your
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Schwarzweller, Christoph, and Artur Korniłowicz. "Characteristic of Rings. Prime Fields." Formalized Mathematics 23, no. 4 (2015): 333–49. http://dx.doi.org/10.1515/forma-2015-0027.

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Summary The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.
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Putra, Zetra Hainul. "Didactic Transposition of Rational Numbers: a Case From a Textbook Analysis and Prospective Elementary Teachers’ Mathematical and Didactic Knowledge." Revija za elementarno izobraževanje 13, no. 4 (2020): 365–94. http://dx.doi.org/10.18690/rei.13.4.365-394.2020.

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This study aims to present a detailed analysis of didactic transposition of rational numbers from knowledge to be taught into taught knowledge occurring in a teacher education institution. The knowledge to be taught of rational numbers is analysed from the mathematics textbook used by prospective elementary teachers in a mathematics education course. The analysis focuses on mathematical praxeology, especially the type of task and technique. Then, the taught knowledge is investigated from 32 prospective elementary teachers’ collaborative work on two hypothetical teacher tasks (HTT) related to o
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Nowlin, Douald. "Division with Fractions." Mathematics Teaching in the Middle School 2, no. 2 (1996): 116–19. http://dx.doi.org/10.5951/mtms.2.2.0116.

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Although operations with fractions have been in the elementary and middle school curriculum for many years, finding examples of practical problems that illustrate the usefulness of division with fractions and mixed numbers is not easy. Most real-world applications of rational numbers involve decimal numerals (Usiskin and Bell 1984), but examples of division with fractions and mixed numbers are often obviously contrived. In addition, many teachers and prospective teachers have difficulty constructing examples and concrete models for the operation of division with fractions (Borko 1992; Ball 198
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Gorbunov, Konstantin, and Vassily Lyubetsky. "Linear Time Additively Exact Algorithm for Transformation of Chain-Cycle Graphs for Arbitrary Costs of Deletions and Insertions." Mathematics 8, no. 11 (2020): 2001. http://dx.doi.org/10.3390/math8112001.

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We propose a novel linear time algorithm which, given any directed weighted graphs a and b with vertex degrees 1 or 2, constructs a sequence of operations transforming a into b. The total cost of operations in this sequence is minimal among all possible ones or differs from the minimum by an additive constant that depends only on operation costs but not on the graphs themselves; this difference is small as compared to the operation costs and is explicitly computed. We assume that the double cut and join operations have identical costs, and costs of the deletion and insertion operations are arb
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Chung, Heewon, and Myungsun Kim. "Encoding of Rational Numbers and Their Homomorphic Computations for FHE-Based Applications." International Journal of Foundations of Computer Science 29, no. 06 (2018): 1023–44. http://dx.doi.org/10.1142/s0129054118500193.

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This work addresses a basic problem of security systems that operate on very sensitive information. Specifically, we are interested in the problem of privately handling numeric data represented by rational numbers (e.g., medical records). Fully homomorphic encryption (FHE) is one of the natural and powerful tools for ensuring privacy of sensitive data, while allowing complicated computations on the data. However, because the native plaintext domain of known FHE schemes is restricted to a set of quite small integers, it is not easy to obtain efficient algorithms for encrypted rational numbers i
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Yakes, Christopher. "Rational Number Operations on the Number Line." Mathematics Enthusiast 14, no. 1-3 (2017): 309–24. http://dx.doi.org/10.54870/1551-3440.1400.

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Jay, Ar I. Laranang Edd, En Jay B. Santiago Prince, Louise Oca Danielle, and Vincent T. Bongon Patrick. "Math SCRABBLE (Strengthening Critical Thinking and Problem-Solving, Reinforcing Rational Numbers and Integers, Applying Basic Operations for Building Learner's Excellence in Mathematics)." International Journal of Social Science and Education Research Studies 05, no. 05 (2025): 435–44. https://doi.org/10.5281/zenodo.15469834.

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Abstract : This action research explores the impact of an innovative game-based intervention entitled “Math SCRABBLE (Strengthening Critical Thinking and Problem-Solving, Reinforcing Rational Numbers and Integers, Applying Basic Operations for Building Learner’s Excellence in Mathematics),” on the academic performance of grade 7 students at Mount Carmel College of Casiguran, Inc., academic year 2024-2025. The research employs a quasi-experimental design with purposive sampling consisting of an experimental and control group, wherein the experimental group undergoes the interv
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Carvalho, Alexia Bezerra de, Rita de Cássia da Costa Guimarães, William Vieira, Emanoel Fabiano Menezes Pereira, and Roberto Seidi Imafuku. "Sobre dificuldades de ingressantes no ensino médio na compreensão de números racionais." ForScience 9, no. 1 (2021): e00878. http://dx.doi.org/10.29069/forscience.2021v9n1.e878.

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Apresenta-se, neste artigo, uma análise da resolução de uma questão sobre números racionais, exposta por estudantes ingressantes no Ensino Médio. O objetivo foi identificar as principais dificuldades e erros apresentados pelos participantes sobre o conceito e operações de números racionais. Para isso, realizou-se uma análise de erros das resoluções apresentadas pelos participantes. A interação de aspectos algorítmicos, intuitivos e formais é o referencial teórico adotado nas análises. Verificou-se que os estudantes não possuem clareza sobre o conceito de número racional e apresentam, em decorr
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Rozprawy doktorskie na temat "Operations on rational numbers"

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Dopico, Evelyn. "The Impact of Small Group Intervention Focusing on Operations with Rational Numbers on Students' Performance in the Florida Algebra I End-of-Course Examination." Thesis, Nova Southeastern University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10845405.

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<p> In Florida, passing the Algebra I end-of-course examination (EOCE) is a graduation requirement. The test measures knowledge of basic algebra. In spring 2015, the Department of Education introduced a different version of the test. For the first two administrations of the new test, the failure rate for 9th-grade students in the state was almost 50%. In contrast, the failure rate for students in the school where this study was implemented exceeded 70%. The purpose of this study was to determine the outcome of small group intervention focusing on operations with rational numbers of high schoo
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Lopes, Ana Paula. "Desenvolvimento do sentido de número no ensino básico: um estudo no sétimo ano de escolaridade." Master's thesis, Universidade de Évora, 2010. http://hdl.handle.net/10174/20773.

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A sociedade contemporânea exige do cidadão raciocínio quantitativo e os novos paradigmas económico-sociais colocam a Matemática escolar perante um novo desafio: desenvolver a literacia matemática dos alunos. A literacia matemática contempla um vasto conjunto de conhecimentos e capacidades entre eles o sentido de número. O desenvolvimento do sentido de número dos alunos tem suscitado alguns trabalhos de pesquisa, em particular ao nível do primeiro e segundo ciclos do Ensino Básico. O objectivo desde estudo é recolher evidências sobre o sentido de número de alunos do terceiro ciclo, mais concret
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Coward, Daniel R. "Sums of two rational cubes." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320587.

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Ketkar, Pallavi S. (Pallavi Subhash). "Primitive Substitutive Numbers are Closed under Rational Multiplication." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278637/.

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Lehr (1991) proved that, if M(q, r) denotes the set of real numbers whose expansion in base-r is q-automatic i.e., is recognized by an automaton A = (Aq, Ar, ao, δ, φ) (or is the image under a letter to letter morphism of a fixed point of a substitution of constant length q) then M(q, r) is closed under addition and rational multiplication. Similarly if we let M(r) denote the set of real numbers α whose base-r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution then in an
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Brown, Bruce John Lindsay. "The initial grounding of rational numbers : an investigation." Thesis, Rhodes University, 2007. http://hdl.handle.net/10962/d1006351.

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This small scale exploratory research project investigated the grounding of rational number concepts in informal, everyday life situations. A qualitative approach was taken to allow for the identification and then in depth investigation, of issues of importance for such a grounding of rational number understanding. The methodology followed could be seen as a combination of grounded theory and developmental research. And the data was generated through in-depth and clinical interviews structured around a number of grounded tasks related to rational numbers. The research comprised three cycles of
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LORIO, MARCELO NASCIMENTO. "APPROXIMATIONS OF REAL NUMBERS BY RATIONAL NUMBERS: WHY THE CONTINUED FRACTIONS CONVERGING PROVIDE THE BEST APPROXIMATIONS?" PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2014. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=23981@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>Frações Contínuas são representações de números reais que independem da base de numeração escolhida. Quando se trata de aproximar números reais por frações, a escolha da base dez oculta, frequentemente, aproximações mais eficientes do que as exibe. Integrar conceitos de aproximações de números reais por frações contínuas com aspectos geométricos traz ao assunto uma abordagem diferenciada e bastante esclarecedora. O algoritmo de Euclides, por exemplo, ao ganhar significado geomé
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Trappmann, Henryk. "Arborescent numbers : higher arithmetic operations and division trees." Phd thesis, Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2007/1524/.

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The overall program "arborescent numbers" is to similarly perform the constructions from the natural numbers (N) to the positive fractional numbers (Q+) to positive real numbers (R+) beginning with (specific) binary trees instead of natural numbers. N can be regarded as the associative binary trees. The binary trees B and the left-commutative binary trees P allow the hassle-free definition of arbitrary high arithmetic operations (hyper ... hyperpowers). To construct the division trees the algebraic structure "coppice" is introduced which is a group with an addition over which the multiplicatio
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Hellman, Noah. "Mitchell-Based Approximate Operations on Floating-Point Numbers." Thesis, Linköpings universitet, Datorteknik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-178882.

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By adapting Mitchell's algorithm for floating-point numbers, one can efficiently perform arithmetic floating-point operations in an approximate logarithmic domain in order to perform approximate computations of functions such as multiplication, division, square root and others. This work examines how this algorithm can be improved in terms of accuracy and hardware complexity by applying a set of various methods that are parametrized and offer a large design space. Optimal coefficients for a large portion of this space is determined and used to synthesize circuits for both ASIC and FPGA circuit
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Carbone, Rose Elaine. "Elementary Teacher Candidates’ Understanding of Rational Numbers: An International Perspective." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79565.

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This paper combines data from two different international research studies that used problem posing in analyzing elementary teacher candidates’ understanding of rational numbers. In 2007, a mathematics educator from the United States and a mathematician from Northern Ireland collaborated to investigate their respective elementary teacher candidates’ understanding of addition and division of fractions. A year later, the same US mathematics educator collaborated with a mathematics educator from South Africa on a similar research project that focused solely on the addition of fractions. The resul
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Clark, David Alan. "The Euclidean algorithm for Galois extensions of the rational numbers." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=39408.

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Let K be a totally real, quartic, Galois extension of $ doubq$ whose ring of integers R is a principal ideal domain. If there is a prime ideal p of R such that the unit group maps onto $(R/{ bf p} sp2$)*, then R is a Euclidean domain. This criterion is generalized to arbitrary Galois extensions.<br>Let E be an elliptic curve over a number field F. Suppose ($F: doubq rbrack le 4$ and $F(E lbrack q rbrack ) not subseteq F$ for all primes q such that F contains a primitive $q sp{ rm th}$ root of unity, then the reduced elliptic curve $ tilde{E}(F sb{ bf p})$ is cyclic infinitely often. In general
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Książki na temat "Operations on rational numbers"

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S, Bezuk Nadine, ed. Understanding rational numbers and proportions. National Council of Teachers of Mathematics, 1994.

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Mary, Stroh, and Sopris West Inc, eds. TransMath: Making sense of rational numbers. Cambium Learning/Sopris West, 2010.

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P, Carpenter Thomas, Fennema Elizabeth, and Romberg Thomas A, eds. Rational numbers: An integration of research. Lawrence Erlbaum Associates, 1992.

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Lappan, Glenda. Bits and pieces I: Understanding rational numbers. Dale Seymour Publications, 1998.

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Glenda, Lappan, and Michigan State University, eds. Bits and pieces II: Using rational numbers. Dale Seymour Publications, 1998.

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Lappan, Glenda. Bits and pieces I: Understanding rational numbers. Dale Seymour Publications, 1998.

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Glenda, Lappan, and Michigan State University, eds. Bits and pieces II: Using rational numbers. Prentice Hall, 2002.

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1948-, Silver Edward A., and Stein Mary Kay, eds. Improving instruction in rational numbers and proportionality. Teachers College Press, 2005.

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Bellos, Alex. Here's looking at Euclid: A surprising excursion through the astonishing world of math. Free Press, 2010.

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Bellos, Alex. Here's Looking at Euclid: A Surprising Excursion through the Astonishing World of Math. Free Press, 2010.

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Części książek na temat "Operations on rational numbers"

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Krasa, Nancy, Karen Tzanetopoulos, and Colleen Maas. "Rational Numbers and Operations." In How Children Learn Math. Routledge, 2022. http://dx.doi.org/10.4324/9781003157656-15.

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Lehrer, Richard, and Leona Schauble. "Measurement Models of Arithmetic Operations and Rational Number." In Measuring and Visualizing Space in Elementary Mathematics Learning. Routledge, 2023. http://dx.doi.org/10.4324/9781003287476-7.

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Jakobsen, Peter Viggo. "Deterrence in Peace Operations: Look Beyond the Battlefield and Expand the Number of Targets and Influence Mechanisms." In NL ARMS. T.M.C. Asser Press, 2020. http://dx.doi.org/10.1007/978-94-6265-419-8_17.

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AbstractThe peace operations literature suffers from a narrow focus on battlefield deterrence. It ignores the need to deter actors beyond the battlefield from supporting the combatants using force, and analyses the use of military threats and force in peace operations in a vacuum without taking into account the other instruments that deterring actors employ simultaneously to influence the combatants, combatant allies, combatant supporters and bystanders that undermine deterrence in peace operations. Since most peace operation forces lack the capacity and willingness to threaten and use force i
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Ye, Weijia, Rubiao Han, Peng Gao, and Ning He. "Research on Airport Communication and Navigation Equipment Inspection Assistance System Based on AR Technology." In Lecture Notes in Electrical Engineering. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-96-2409-6_6.

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Abstract Aviation transportation is an important component of our country’s transportation system. With the rapid improvement of the national economy, the civil aviation industry in our country has experienced rapid development, and the number and scale of airports are also constantly increasing. Communication and navigation systems play an important role in the transportation of aircraft and the scale operation of airports. Efficient and accurate communication and navigation system can not only effectively ensure air transportation safety but also improve overall operational efficiency, makin
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Eriksson, Kenneth, Donald Estep, and Claes Johnson. "Rational Numbers." In Applied Mathematics: Body and Soul. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05796-4_7.

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Bhattacharjee, Meenaxi, Rögnvaldur G. Möller, Dugald Macpherson, and Peter M. Neumann. "Rational Numbers." In Notes on Infinite Permutation Groups. Hindustan Book Agency, 1997. http://dx.doi.org/10.1007/978-93-80250-91-5_9.

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Bhattacharjee, Meenaxi, Dugald Macpherson, Rögnvaldur G. Möller, and Peter M. Neumann. "Rational numbers." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0092559.

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Shah, Nita H., and Vishnuprasad D. Thakkar. "Rational Numbers." In Journey from Natural Numbers to Complex Numbers. CRC Press, 2020. http://dx.doi.org/10.1201/9781003105244-3.

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Noël, Marie-Pascale, and Giannis Karagiannakis. "Rational numbers." In Effective Teaching Strategies for Dyscalculia and Learning Difficulties in Mathematics. Routledge, 2022. http://dx.doi.org/10.4324/b22795-6.

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Ovchinnikov, Sergei. "Rational Numbers." In Real Analysis: Foundations. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-64701-8_1.

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Streszczenia konferencji na temat "Operations on rational numbers"

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Chawdhry, Herschel. "Interpolation of rational functions in loop calculations by using p-adic numbers." In Loops and Legs in Quantum Field Theory. Sissa Medialab, 2024. http://dx.doi.org/10.22323/1.467.0037.

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Roti, J. S., and M. M. Mullins. "Operating Experiences in Treating Alkaline, No pH Control Cooling Water Systems." In CORROSION 1989. NACE International, 1989. https://doi.org/10.5006/c1989-89158.

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Abstract Alkaline, no-pH control cooling water treatment applications represent a growing market in today's industrial environment. Many plants prefer to not feed acid to their open recirculating cooling systems to destroy alkalinity and lower pH because of the inherent handling and safety considerations of this material. Other plants view the use of acid as just another source of system upset should this material be over or under fed. This paper reviews the rationale of why more facilities are moving to this technology, outlines a number of treatment programs which are available to effectivel
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Manouchehri, Soheil. "Subsea Pipelines and Flowlines Decommissioning: What We Should Know for a Rational Approach." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61239.

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Offshore and subsea decommissioning will increase in the next five years or so as many producing fields are matured and cease production while the oil price continues to remain low. This emphasizes the need for a thorough decommissioning plan to ensure a safe and technically feasible solution while it is economically viable and safeguards the environment. Offshore and subsea decommissioning is commonly considered on a case-by-case basis using the Comparative Assessment (CA) process in which the best decommissioning solution is obtained. Health, Safety and Environmental (HSE) considerations are
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Cantamessa, Marco, and Francesca Montagna. "Beyond Lean Manufacturing: Developing an Integrated Methodology to Design Effective Manufacturing Systems." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59223.

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Global competition forces manufacturing companies to operate deep changes in their production systems, involving physical resources, operating procedures and the organization. In this context, the Lean Manufacturing (LM) paradigm is quite popular and lean practice efforts have crossed from the automotive sector into other industries. Most academic contributions to literature concerning LM are on specific aspects of LM, while there is little discussion on the overall implementation of LM. This is despite the fact that lean principles encompass all aspects of manufacturing operations and the nee
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ȚARĂLUNGĂ, Boris. "Rational numbers that are not represented as the sum of unit rational fractions." In "Ştiință și educație: noi abordări și perspective", conferinţă ştiinţifică internaţională. Ion Creangă Pedagogical State University, 2024. https://doi.org/10.46727/c.v4.21-22-03-2024.p68-72.

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Tsakatikas, D., and M. Sfantsikopoulos. "Development of a Decision Support System for Unscheduled Maintenance MRO Component Safety Stock." In ASME 2007 International Manufacturing Science and Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/msec2007-31115.

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The paper presents a methodology for the establishment of the MRO (Maintenance, Repair and Operation) material criticality that is focused on the Industrial Unplanned Maintenance needs. The thus obtained criticality is used to rationalize the efficiency of the Plant MRO-material Inventory. Through an appropriately adapted Top-Down FMECA (Failure Modes Effects and Criticality Analysis) the concept of the Component Dynamic Criticality is introduced and calculated for all the functional components of an industrial production facility. The components are assigned with characteristic code numbers.
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Vălcan, Teodor-Dumitru. "Structures of Fields of Rational Numbers, Isomorphic Between Them." In 10th International Conference Education, Reflection, Development. European Publisher, 2023. http://dx.doi.org/10.15405/epes.23056.8.

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Pion, Sylvain, and Chee K. Yap. "Constructive root bound for k-ary rational input numbers." In the nineteenth conference. ACM Press, 2003. http://dx.doi.org/10.1145/777792.777831.

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Adishamita, Rasi, Mashadi Mashadi, and Muliana Muliana. "New Formula for Interval Numbers with Powers of Positive Rational Numbers and Its Properties." In Proceedings of the 3rd Sriwijaya International Conference on Basic and Applied Sciences, SICBAS 2023, November 3, 2023, Palembang, Indonesia. EAI, 2024. http://dx.doi.org/10.4108/eai.3-11-2023.2347908.

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Yokoyama, Ryohei, and Koichi Ito. "Evaluation of Operational Performance of Gas Turbine Cogeneration Plants Using an Optimization Tool: OPS-Operation." In ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/gt2003-38381.

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To attain the highest performance of gas turbine cogeneration plants, it is necessary to rationally select the numbers and capacities of gas turbines and auxiliary equipment in consideration of their operational strategies corresponding to energy demands which change with season and time. It is also important to rationally select the options such as the variable heat to power by the steam injection or combined cycle, and the inlet air cooling by the ice storage combined with electric compression refrigeration or steam absorption refrigeration. The evaluation of the effects of these alternative
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Raporty organizacyjne na temat "Operations on rational numbers"

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Rosenfeld. L51741 Development of a Model for Fatigue Rating Shallow Unrestrained Dents. Pipeline Research Council International, Inc. (PRCI), 1997. http://dx.doi.org/10.55274/r0010337.

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The ability to fatigue-rate dents in line pipe is important for three reasons. First, field failures give evidence that fatigue crack growth occurs in dents under certain circumstances in spite of the fact that plain dents are generally thought to have little effect on the integrity of natural gas pipelines based on the results of single-cycle burst tests. Second, many operators are discovering large numbers of dents on the bottom quadrants of their pipe associated with rocks and backfill loads. Guidance is needed for discerning dents for which excavation and inspection is economically wastefu
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NATIONAL WAR COLL WASHINGTON DC. Fixing US Special Operations. Rational Actors Not Allowed. Defense Technical Information Center, 1993. http://dx.doi.org/10.21236/ada441771.

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Satogata, T. RHIC RF Harmonic Numbers for Low Energy Operations. Office of Scientific and Technical Information (OSTI), 2008. http://dx.doi.org/10.2172/939977.

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Satogata T. RHIC RF Harmonic Numbers For Low Energy Operations. Office of Scientific and Technical Information (OSTI), 2008. http://dx.doi.org/10.2172/1061899.

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Lu, Chao. A Computational Library Using P-adic Arithmetic for Exact Computation With Rational Numbers in Quantum Computing. Defense Technical Information Center, 2005. http://dx.doi.org/10.21236/ada456488.

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Smit, Timo, Sofia Sacks Ferrari, and Jaïr van der Lijn. Trends in Multilateral Peace Operations, 2019. Stockholm International Peace Research Institute, 2020. http://dx.doi.org/10.55163/ixjs4170.

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Despite evidence of their positive impacts, United Nations peacekeeping operations continue to face budget cuts, cynicism in the political arena and concern over personnel physical safety. This context underpins the global and regional trends in multilateral peace operations in 2019. This SIPRI Fact Sheet gives a snapshot of multilateral peace operations in 2019, with statistics on personnel, country contributions and fatalities for operations conducted by the UN, regional organizations or alliances, and ad hoc coalitions of states. Global and regional trends in 2019 follow developments from r
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Lutz, Carsten. Adding Numbers to the SHIQ Description Logic - First Results. Aachen University of Technology, 2001. http://dx.doi.org/10.25368/2022.117.

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Recently, the Description Logic (DL) SHIQ has found a large number of applications. This success is due to the fact that SHIQ combines a rich expressivity with efficient reasoning, as is demonstrated by its implementation in DL systems such as FaCT and RACER. One weakness of SHIQ, however, limits its usability in several application areas: numerical knowledge such as knowledge about the age, weight, or temperature of real-world entities cannot be adequately represented. In this paper, we propose an extension of SHIQ that aims at closing this gap. The new Description Logic Q-SHIQ, which augment
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Soder, Kirsten. Multilateral Peace Operations: Personnel, 2009. Stockholm International Peace Research Institute, 2010. http://dx.doi.org/10.55163/anmf8652.

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This SIPRI Fact Sheet presents data from the SIPRI Multilateral Peace Operations Database to illuminate some of the most significant developments in peace operations personnel in 2009 as well as trends over the decade since 2000. It includes statistical data on numbers and type of peacekeeping personnel, the organizations and countries mounting operations and deploying personnel.
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Soder, Kirsten. Multilateral Peace Operations: Europe, 2009. Stockholm International Peace Research Institute, 2010. http://dx.doi.org/10.55163/wkwc3096.

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This SIPRI Fact Sheet presents data from the SIPRI Multilateral Peace Operations Database to illuminate some of the most significant developments in peace operations in Europe in 2009 as well as trends over the decade since 2000. It includes statistical data on numbers and type of peacekeeping personnel, the organizations and countries mounting operations and deploying personnel, along with maps of peace operations that were active during 2009.
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Soder, Kirsten. Multilateral Peace Operations: Asia, 2009. Stockholm International Peace Research Institute, 2010. http://dx.doi.org/10.55163/zsky7548.

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This SIPRI Fact Sheet presents data from the SIPRI Multilateral Peace Operations Database to illuminate some of the most significant developments in peace operations in Asia in 2009 as well as trends over the decade since 2000. It includes statistical data on numbers and type of peacekeeping personnel, the organizations and countries mounting operations and deploying personnel, along with maps of peace operations that were active during 2009.
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