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Автор: Grafiati

Опубліковано: 11 вересня 2023

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Статті в журналах з теми "ARITHMETIC EXPRESSION"

Guo, Ping, and Sheng Jiao Liu. "Arithmetic Expression Evaluation in Membrane Computing with Priority." Advanced Materials Research 225-226 (April 2011): 1115–19. http://dx.doi.org/10.4028/www.scientific.net/amr.225-226.1115.

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Arithmetic operation and arithmetic expression evaluation are basic operations of a computing model. Based on the rules with priority, this paper discusses arithmetic operation and arithmetic expression evaluation in transition P system. We present the rules of arithmetic operation and the arithmetic of constructing arithmetic expression evaluation’s membrane structure based on the arithmetic operation rules. In the arithmetic operation rules, we use some specifically symbols to make rules applied in a maximally parallel manner, and also assure synchronization need during the rules application.

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Kosolapov, Yury V. "On Simplifying Expressions with Mixed Boolean-Arithmetic." Modeling and Analysis of Information Systems 30, no. 2 (June 14, 2023): 140–59. http://dx.doi.org/10.18255/1818-1015-2023-2-140-159.

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Mixed Boolean-Arithmetic expressions (MBA-expressions) with $t$ integer $n$-bit variables are often used for program obfuscations. Obfuscation consists of replacing short expressions with longer equivalent expressions that seem to take the analyst more time to explore. The paper shows that to simplify linear MBA-expressions (reduce the number of terms), a technique similar to the technique of decoding linear codes by information sets can be applied. Based on this technique, algorithms for simplifying linear MBA-expressions are constructed: an algorithm for finding an expression of minimum length and an algorithm for reducing the length of an expression. Based on the length reduction algorithm, an algorithm is constructed that allows to estimate the resistance of an MBA-expression to simplification. We experimentally estimate the dependence of the average number of terms in a linear MBA-expression returned by simplification algorithms on $n$, the number of decoding iterations, and the power of the set of Boolean functions, by which a linear combination with a minimum number of nonzero coefficients is sought. The results of the experiments for all considered $t$ and $n$ show that if before obfuscation the linear MBA-expression contained $r=1,2,3$ terms, then the developed simplification algorithms with a probability close to one allow using the obfuscated version of this expression find an equivalent one with no more than $r$ terms. This is the main difference between the information set decoding technique and the well-known techniques for simplifying linear MBA-expressions, where the goal is to reduce the number of terms to no more than $2^t$. We also found that for randomly generated linear MBA-expressions with increasing $n$, the average number of terms in the returned expression tends to $2^t$ and does not differ from the average number of terms in the linear expression returned by known simplification algorithms. The results obtained, in particular, make it possible to determine $t$ and $n$ for which the number of terms in the simplified linear MBA-expression on average will not be less than the given one.

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Guo, Ping, and Hai-Zhu Chen. "Arithmetic Expression Evaluation by P Systems." Applied Mathematics & Information Sciences 7, no. 2L (June 1, 2013): 549–53. http://dx.doi.org/10.12785/amis/072l26.

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Peretiaha, Maksym, Mykyta Poltavets, Kirill Smelyakov, and Anastasia Chupryna. "SYNTACTIC ANALYSIS OF ARITHMETIC EXPRESSIONS FOR OPTIMIZING THE OPERATION OF PROGRAMS." Grail of Science, no. 26 (April 23, 2023): 215–29. http://dx.doi.org/10.36074/grail-of-science.14.04.2023.039.

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Our algorithm combines the Reverse Polish Notation (RPN) and expression tree algorithms it is a novel method for efficiently evaluating arithmetic expressions. The algorithm combines the benefits of Reverse Polish Notation (RPN) and Expression Trees to provide a practical and efficient solution for evaluating expressions in both infix and postfix notation. The algorithm first converts the infix notation to RPN, which is then used to construct an expression tree. The expression tree is evaluated using a recursive function that traverses the tree and performs the required operations. The use of an expression tree allows for the optimization of sub-expressions, further improving the efficiency of the algorithm. The Combined RPN and Expression Tree Algorithm offers several advantages over other algorithms for evaluating arithmetic expressions. It is more efficient than some recursive algorithms while being more practical than stack-based algorithms. Furthermore, the use of an expression tree allows for the optimization of sub-expressions, further improving efficiency.

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Ali, Hassan, Muhammad Shumail Naveed, Dilawar Naseem, and Jawaid Shabbir. "LL (1) Parser versus GNF inducted LL (1) Parser on Arithmetic Expressions Grammar: A Comparative Study." Quaid-e-Awam University Research Journal of Engineering, Science & Technology 18, no. 02 (December 31, 2020): 89–101. http://dx.doi.org/10.52584/qrj.1802.14.

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The prime objective of the proposed study is to determine the induction of Greibach Normal Form (GNF) in Arithmetic Expression Grammars to improve the processing speed of conventional LL(1) parser. Conventional arithmetic expression grammar and its equivalent LL(1) is used in the study which is converted. A transformation method is defined which converts the selected grammar into a Greibach normal form that is further converted into a GNF based parser through a method proposed in the study. These two parsers are analyzed by considering 399 cases of arithmetic expressions. During statistical analysis, the results are initially examined with the Kolmogorov-Smirnov and Shapiro-Wilk test. The statistical significance of the proposed method is evaluated with the Mann-Whitney U test. The study described that GNF based LL(1) parser for arithmetic take fewer steps than conventional LL(1) grammar. The ranks and asymptotic significance depict that the GNF based LL(1) method is significant than the conventional LL(1) approach. The study adds to the knowledge of parsers itself, parser expression grammars (PEG’s), LL(1) grammars, Greibach Normal Form (GNF) induced grammar structure, and the induction of Arithmetic PEG’s LL(1) to GNF based grammar.

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Liu, Binbin, Qilong Zheng, Jing Li, and Dongpeng Xu. "An In-Place Simplification on Mixed Boolean-Arithmetic Expressions." Security and Communication Networks 2022 (September 14, 2022): 1–14. http://dx.doi.org/10.1155/2022/7307139.

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Mixed Boolean-arithmetic (MBA) expression, which involves both bitwise operations (e.g., NOT, AND, and OR) and arithmetic operations (e.g., + , − , and ∗ ), is a software obfuscation scheme. On the other side, multiple methods have been proposed to simplify MBA expressions. Among them, table-based solutions are the most powerful simplification research. However, a fundamental limitation of the table-based solutions is that the space complexity of the transformation table drastically explodes with the number of variables in the MBA expression. In this study, we propose a novel method to simplify MBA expressions without any precomputed requirements. First, a bitwise expression can be transformed into a unified form, and we provide a mathematical proof to guarantee the correctness of this transformation. Then, the arithmetic reduction is smoothly performed to further simplify the expression and produce a concise result. We implement the proposed scheme as an open-source tool, named MBA-Flatten, and evaluate it on two comprehensive benchmarks. The evaluation results show that MBA-Flatten is a general and effective MBA simplification method. Furthermore, MBA-Flatten can assist malware analysis and boost SMT solvers’ performance on solving MBA equations.

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BAI, Yu, and Xian'e GUO. "Lightweight evaluation algorithm for infix arithmetic expression." Journal of Computer Applications 33, no. 11 (November 26, 2013): 3163–66. http://dx.doi.org/10.3724/sp.j.1087.2013.03163.

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Cseresnyes, Ehud, and Hannes Seiwert. "Regular expression length via arithmetic formula complexity." Journal of Computer and System Sciences 125 (May 2022): 1–24. http://dx.doi.org/10.1016/j.jcss.2021.10.004.

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Pradeep, B., and C. Siva Ram Murthy. "Parallel arithmetic expression evaluation on reconfigurable meshes." Computer Languages 20, no. 4 (November 1994): 267–77. http://dx.doi.org/10.1016/0096-0551(94)90008-6.

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Dabić-Boričić, Milana, and Marijana Zeljić. "Modelovanje ekvivalencije matematičkih izraza u početnoj nastavi." Inovacije u nastavi 34, no. 2 (2021): 30–43. http://dx.doi.org/10.5937/inovacije2101030d.

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The notion of expression equivalence is one of the terms that has been recognized in the literature as key to understanding algebraic ideas. To understand this term, the context used as a basis for developing meaning is important, as well as the language in which generalizations are expressed. The aim of this paper is twofold: a) to examine whether the context of a textual task and modeling activities influence the understanding of the transformation of expressions into equivalent forms; b) determine whether the understanding of the equivalence of the expression is affected by the level of abstractness of the expression (algebraic or arithmetic). The research is of a quasi-experimental design with two experimental groups and one control group. The sample consists of 148 fourth-graders. The existence of statistically significant differences between the students of the experimental groups and the control group suggests that the modeling process influences the development of the notion of expression equivalence. This research did not show any differences in the results of the students who were taught using algebraic or arithmetic expressions. This implies that the understanding of equivalence developed through the modeling process is not related to the level of abstractness of the mathematical language used, but that, based on understanding the meaning of the term, students can transform arithmetic and algebraic expressions with equal success.

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Більше джерел

Дисертації з теми "ARITHMETIC EXPRESSION"

Mouilleron, Christophe. "Efficient computation with structured matrices and arithmetic expressions." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00688388.

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Designing efficient code in practice for a given computation is a hard task. In this thesis, we tackle this issue in two different situations. The first part of the thesis introduces some algorithmic improvements in structured linear algebra. We first show how to extend an algorithm by Cardinal for inverting Cauchy-like matrices to the other common structures. This approach, which mainly relies on products of the type "structured matrix × matrix", leads to a theoretical speed-up of a factor up to 7 that we also observe in practice. Then, we extend some works on Toeplitz-like matrices and prove that, for any of the common structures, the product of an n×n structured matrix of displacement rank α by an n×α matrix can be computed in Õ(α^(ω-1)n). This leads to direct inversion algorithms in Õ(α^(ω-1)n) , that do not rely on a reduction to the Toeplitz-like case. The second part of the thesis deals with the implementation of arithmetic expressions. This topic raises several issues like finding the minimum number of operations, and maximizing the speed or the accuracy when using some finite-precision arithmetic. Making use of the inductive nature of arithmetic expressions enables the design of algorithms that help to answer such questions. We thus present a set of algorithms for generating evaluation schemes, counting them, and optimizing them according to one or several criteria. These algorithms are part of a library that we have developed and used, among other things, in order to decrease the running time of a code generator for a mathematical library, and to study optimality issues about the evaluation of a small degree polynomial with scalar coefficients at a matrix point.

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Jonsson, Josefine. "Att strukturera och beräkna matematiska uttryck : En studie om hur elever i årskurs 5 hanterar utvecklade aritmetiska uttryck." Thesis, Högskolan för lärande och kommunikation, Högskolan i Jönköping, Matematikdidaktik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-30590.

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En del svårigheter som elever upplever i algebra kan bero på saknad förståelse av strukturen i matematiska uttryck. Struktur, i det här sammanhanget, syftar på hur en matematisk enhet består av delar, och hur dessa delar är relaterade till varandra. Tidigare studier indikerar också att elevers svårigheter inom algebra beror på bristande aritmetiska kunskaper. Inom aritmetiken kan elever ofta använda informella metoder, medan algebraiska aktiviteter kräver en större medvetenhet om matematiska strukturer. Man har därför hävdat att elevers svårigheter att hantera algebraiska uttryck kan bero på saknad förståelse av strukturen i aritmetiska uttryck. Syftet med denna studie är att undersöka hur elever i årskurs 5 beräknar och strukturerar utvecklade aritmetiska uttryck, det vill säga, numeriska uttryck med flera räkneoperationer, som exempelvis 5 · 6 + 4 · 2 · 3. I denna studie behandlas numeriska uttryck med tre eller fyra operationer. I studien ingick 116 elever från tre olika skolor. Analysen baseras på data från lösningar av uppgifter på ett skriftligt arbetsblad. Arbetsbladet bestod av tio aritmetiska räkneuppgifter, som eleverna arbetade med individuellt. I analysen av data framkom olika metoder, som eleverna använde för att strukturera och beräkna de aritmetiska uttrycken, speciellt fyra metoder var återkommande i flera uppgifter. Genom de olika tillvägagångssätten som eleverna använde för att beräkna matematiska uttryck kunde olika sätt att skapa struktur upptäckas. Många elever utgick från uttryckens ytliga struktur och endast få elever visade förmåga att urskilja uttryckens dolda struktur.
Some of the difficulties students experience in algebra can be due to lack of understanding of the structure in mathematical expressions. Structure, in this context, refers to how a mathematical entity consists of its parts, and how these parts are related to each other. Previous studies also indicate that students’ difficulties in algebra devolve upon a lack of arithmetical knowledge. In arithmetic, students can manage by using informal methods, while algebraic activities require a greater awareness of mathematical structures. It has therefore been argued that students’ difficulties with algebraic expressions are caused by a lack of knowledge of the structure in arithmetic expressions. The purpose of this study is to investigate how 5th grade students calculate and structure longer arithmetic expressions, meaning numerical expressions with several operations, for example, 5 · 6 + 4 · 2 · 3. This study covers numerical expressions with three or four operations. The study includes 116 students from three different schools. The analysis is based on data from solutions of tasks on a written worksheet. The worksheet consisted of ten arithmetic calculation assignments that the students worked with individually. The analysis of the data revealed different approaches that students used to structure and calculate the arithmetic expressions, particularly four methods were used in several tasks. Through the different approaches that students used to calculate mathematical expressions, different ways to create structure could be discovered. Many students based their calculations on the surface structure of an expression and only a few students seemed to be able to identify the hidden structure of an expression.

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Karlsson, Rebecka. "Vi hör ihop : Hur elever beräknar numeriska uttryck med sina egenskapade räkneregler." Thesis, Högskolan i Jönköping, Högskolan för lärande och kommunikation, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-44530.

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Två vanliga räkneregler som elever lär sig om i matematikundervisningen är prioriteringsregeln och vänster-till-höger-principen. Tidigare forskning har dock visat att elever också använder påhittade regler som vanligtvis inte brukar användas inom matematiken. Syftet med den här studien är att undersöka dessa ”egenskapade” regler. Syftet uppnås genom att studera vad det är för mindre kända räkneregler som eleverna tillämpar samt om hur konsekventa eleverna är i sin användning av en typ av räkneregel. I studien gjorde 55 elever i årskurs 5 ett arbetsblad bestående av fem numeriska uttryck. Av de 55 eleverna använde 16 av dem någon form av regel som gick ut på att tal i de numeriska uttrycken parades ihop. 13 av de här 16 eleverna blev intervjuade om hur de hade tänkt när de löste uppgifterna. Data för studien utgörs därför av elevernas arbetsblad såväl som transkriberingarna från intervjuerna. Studien visar tre olika slags ”regler” som eleverna använder, förutom de vanliga räknereglerna vänster-till-höger-principen och prioriteringsregeln. De tre räknereglerna bygger alla på att tal paras ihop på ett eller annat sätt. Trots att nästan ingen av de 13 eleverna hade fått undervisning om de vanliga räknereglerna, så använder eleverna egna regler som följer logiska strukturer. Dessutom visar studien att de flesta eleverna inte är speciellt konsekventa när det kommer till valet av regel. Många av eleverna väljer att använda olika slags räkneregler för att beräkna uttryck som är uppbyggda på nästan samma sätt.
Two common rules of arithmetic that students learn about in education are the order of operations and the counting from left to right. However, previous research has shown that students also use made-up rules which are not usually used in mathematics. The aim of this study is to investigate the rules of arithmetic created by the students themselves. The aim is achieved by examine what kind of less-known rules of arithmetic that students apply and also how consistent students are in their use of a type of rule. In the study, 55 students did a worksheet consisting of five tasks. In total, 16 of the 55 students used some kind of rule where numbers in the numerical expressions were paired in some way. Furthermore, 13 of the 16 students were interviewed about their way of thinking when solving the tasks. The data therefore consists of the students’ worksheets and transcriptions from the interviews. The study shows that, in addition to the usual conventions left-to-right and order of operations, students use three different kinds of rules of arithmetic. The three rules of arithmetic are based on the principle that numbers are paired in one way or another. Despite that almost none of the 13 students had been taught the conventional rules of arithmetic, most students use own rules that follow logical structures. In addition, the study shows that most students are not particularly consistent when it comes to choosing strategy. Many students choose to use different kind of rules of arithmetic when they are calculating expressions that are structured in almost the same way.

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Маслова, Зоя Іванівна, Зоя Ивановна Маслова, Zoia Ivanivna Maslova та М. М. Яковлев. "Використання польської нотації для зберігання данних та обчислення значень арифметичних і логічних виразів". Thesis, Сумський державний університет, 2017. http://essuir.sumdu.edu.ua/handle/123456789/65685.

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На сьогоднішній день проблема збереження великих об’ємів даних досить актуальна. Кожна велика компанія має свої сервера, на яких вона зберігає необхідну інформацію. Використання польської нотації для збереження арифметичних виразів може значно зменшити обсяги задіяної пам’яті. Якщо оператори мають фіксовану арність, то в такому записі будуть відсутні дужки, та він може бути інтерпретований без неоднозначності.

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Tian, Chao. "Towards effective analysis of big graphs : from scalability to quality." Thesis, University of Edinburgh, 2017. http://hdl.handle.net/1842/29578.

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This thesis investigates the central issues underlying graph analysis, namely, scalability and quality. We first study the incremental problems for graph queries, which aim to compute the changes to the old query answer, in response to the updates to the input graph. The incremental problem is called bounded if its cost is decided by the sizes of the query and the changes only. No matter how desirable, however, our first results are negative: for common graph queries such as graph traversal, connectivity, keyword search and pattern matching, their incremental problems are unbounded. In light of the negative results, we propose two new characterizations for the effectiveness of incremental computation, and show that the incremental computations above can still be effectively conducted, by either reducing the computations on big graphs to small data, or incrementalizing batch algorithms by minimizing unnecessary recomputation. We next study the problems with regards to improving the quality of the graphs. To uniquely identify entities represented by vertices in a graph, we propose a class of keys that are recursively defined in terms of graph patterns, and are interpreted with subgraph isomorphism. As an application, we study the entity matching problem, which is to find all pairs of entities in a graph that are identified by a given set of keys. Although the problem is proved to be intractable, and cannot be parallelized in logarithmic rounds, we provide two parallel scalable algorithms for it. In addition, to catch numeric inconsistencies in real-life graphs, we extend graph functional dependencies with linear arithmetic expressions and comparison predicates, referred to as NGDs. Indeed, NGDs strike a balance between expressivity and complexity, since if we allow non-linear arithmetic expressions, even of degree at most 2, the satisfiability and implication problems become undecidable. A localizable incremental algorithm is developed to detect errors using NGDs, where the cost is determined by small neighbors of nodes in the updates instead of the entire graph. Finally, a rule-based method to clean graphs is proposed. We extend graph entity dependencies (GEDs) as data quality rules. Given a graph, a set of GEDs and a block of ground truth, we fix violations of GEDs in the graph by combining data repairing and object identification. The method finds certain fixes to errors detected by GEDs, i.e., as long as the GEDs and the ground truth are correct, the fixes are assured correct as their logical consequences. Several fundamental results underlying the method are established, and an algorithm is developed to implement the method. We also parallelize the method and guarantee to reduce its running time with the increase of processors.

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Ottes, Aline Brum. "Expressão numérica: a hierarquia das quatro operações matemáticas." Universidade Federal de Santa Maria, 2016. http://repositorio.ufsm.br/handle/1/12435.

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For the development of this work, in the introduction we present a few topics which motivated it, as well as the research problem and its reason. The main objective of this dissertation is to research on the possible reasons for the hierarchy of the four mathematical operations. With this purpose, we attempted to verify if there were some explanations for such hierarchy. Thus, we researched on national and international sites. On this search, we found two articles of interest, namely: “the order of operation in elementary arithmetic” and the thesis “the school mathematics knowledge: operations with the natural numbers in the grade and middle school”, which were formulated comments about them. This research is classified as qualitative and bibliographical descriptive. In the chapter about the theory we presented how the subject numerical expression is explained in some official documents, as well as in textbooks of the Middle School. Since we have not found any reasonable and plausible explanation for such hierarchy, we included a chapter about a historical retrospective on the order of operations and the use of the parenthesis which, in turn, prepared the way for the chapter on a proposal to justify the why of the hierarchy for the four mathematical operations.
Para o desenvolvimento deste trabalho apresentamos na introdução alguns tópicos motivadores da pesquisa, bem como a sua problemática e justificativa. Esta dissertação tem como objetivo principal pesquisar as possíveis justificativas para a hierarquia das quatro operações aritméticas nas expressões numéricas. Para isso buscamos verificar se existia alguma proposta para a justificativa da hierarquia das operações na resolução de expressões numéricas. Assim, realizamos buscas tanto em sites nacionais, como também internacionais. Nessas buscas os trabalhos de interesse que encontramos foram: o artigo Order of operations in elementar arithmetic e a tese “O conhecimento matemático escolar: operações com números naturais (e adjacências) no Ensino Fundamental” os quais foram realizadas descrição e comentários cabíveis a respeito. O tipo de pesquisa é qualitativa, bibliográfica descritiva e, de certa forma, também explicativa. No referencial teórico apresentamos como o conteúdo expressão numérica é colocado em alguns documentos oficiais e livros didáticos do Ensino Fundamental. Como não foi encontrada nenhuma justificativa plausível e completa para a hierarquia das quatro operações nas expressões numéricas, realizamos um capítulo denominado retrospectiva histórica do uso das quatro operações e dos parênteses, neste capítulo descrevemos sobre as quatro operações, e sobre os parênteses que servirá para embasar o próximo capítulo denominado: hierarquia das quatro operações, buscando uma justificativa.

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Weng, Yu-lin, and 翁瑜璘. "Scaffold of Annotated Arithmetic Expression Directed Posing of Elementary Mathematic Word Problems." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/57265094417743543325.

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碩士
國立中央大學
網路學習科技研究所
96
This research aimed to investigate the influence of Annotated Arithmetic Expression Problem-Posing material on fourth grade students’ problem-posing and problem-solving ability. The posing scaffolding is designed base on the concept and representation of solution tree. In order to understand the effects of this problem-posing material, the first experiment is executed by individual text learning. The statement analysis is done on pre-tests and pose-tests of mathematical-solving ability. Students’ compositions and feedbacks about problem-posing are collected. The experimenter explore the following themes：(1) Students can pose the word problem by material successfully. (2) The opuses of students are correct and can be solved by others. (3) The learning motivation and attitude of students are positive. (4) Problem-posing teaching technique seems to affect students’ problem solving ability. After the experiment, the computer-based problem-posing system with Annotated Arithmetic Expression is implemented in the traditional classroom. The aim of this system is to improve the drawback and the limits of text experiment. This system can work successfully and vividly in guiding students to complete the activities of problem posing, opuses display, and peer problem solving.

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JAIN, ANKIT KUMAR. "MULTI FACTOR MODEL FOR AUTHENTICATION IN SECURITY OF CLOUDS." Thesis, 2014. http://dspace.dtu.ac.in:8080/jspui/handle/repository/15627.

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In this dissertation, we present a layered framework for cloud security. Cloud computing is a new way to deliver services over the internet. Cloud computing architecture gives a proper management to share and distribute all available resources and services over the whole world via computer network. Authentication is a key factor for security, which is a mechanism to establish connection that authenticates the person‟s identity. Traditional authentication approaches are not good enough to provide strong information security in modern cyber-attacks.A number of well-known protocols for authentication are considered the next-generation mobile and computer network services. The potential weaknesses of current existing protocols can be solved by categorization of services and authentication levels in terms of their significance and confidentiality. This can offers mutual and also two-factor authentication that is considered more secure against various phishing attempts than existing authentication protocol. We propose a new level wise authentication imposing several factors for cloud computing. This proposed framework provides efficient and feasible mechanism which can be easily integrated into existing password authentication techniques. This proposed framework is verified by cloud server which authenticates user data. We are using several factors like arithmetic expression, one time password and magic number.

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Zhou, Zheng. "Equivalence checking of arithmetic expressions with applications in DSP synthesis." 1996. https://scholarworks.umass.edu/dissertations/AAI9619461.

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Numerous formal verification systems have been proposed and developed for FSM based control units (notably SMV (71) as well as others). However, most research on the equivalence checking of datapaths is still confined to the bit- or word-level. Formal verification of arithmetic expressions and synthesized datapaths, especially considering finite word-length computation, has not been addressed. Thus formal verification techniques have been prohibited from more extensive applications in numerical and Digital Signal Processing. In this dissertation a formal system, called Conditional Term Rewriting on Attribute Syntax Trees (ConTRAST) is developed and demonstrated for verifying the equivalence between two differently synthesized datapaths. This result arises from a sophisticated integration of three key techniques: attribute grammars, which contribute expressive data structures for syntactic and semantic information about designed datapaths, term rewrite systems, which transform functionally equivalent datapaths into the same canonical form, and LR parsing, which provides an efficient tool for integrating the attribute grammar and the term rewriting system. Unlike other canonical representations, such as BDD (15), and BMD$\sp*$ (17), ConTRAST makes canonicity by manipulating symbolic expressions instead of enumerating values of expressions at the bit- or word-level. Furthermore, the effect of finite word-lengths and their associated arithmetic precision are also considered in the definition of equivalence classes. As a particular application of ConTRAST, a DSP design verification tool called Fixed-Point Verifier (FPV) has been developed. Similar to present DSP hardware design tools, FPV allows users to describe filters in the form of arithmetic expressions and to specify arbitrary fixed-point wordlengths on various signals. However, unlike simulation-based verification methods like Cadence/Alta's Fixed Point Optimizer and Mentor's DSPstation, FPV can automatically perform correctness-checking and equivalence-checking for a given filter design under the effect of finite word length.

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Benešová, Jana. "Jevy, které mají vliv na úspěšnost žáka při řešení úloh s algebraickými výrazy." Master's thesis, 2015. http://www.nusl.cz/ntk/nusl-345093.

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This thesis focuses on errors and difficulties that students face when solving problems with algebraic expressions in mathematics at secondary school. Its aim was to describe the factors that affect pupils' achievement while dealing with algebraic expressions, classify them on the basis of a classification of pupils' errors used in mathematics and identify the biggest pupils' difficulties. The thesis consists of theoretical and experimental parts. The theoretical part focuses on the factors that influence the success of pupils in their learning process. I present their summary based on information gained from literature and I complete them with my own teaching experience of mathematics at secondary school. Next I deal with the concept of error, error classification and one of the most important phases of learning process, which is a description of teacher's work with pupil's error (again on the basis of information gained from the literature). The theoretical part ends with definitions of basic concepts from specialized literature on algebraic expressions at the end of the theoretical part. In the experimental part I deal with my own experiment during teaching of mathematics at secondary school, which is based on individual written work of students in the first year of their study and on the...

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Книги з теми "ARITHMETIC EXPRESSION"

Pietroski, Paul M. Semantic Typology and Composition. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198739548.003.0011.

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How many types of expression meaning are there, and are some types more basic than others? According to a familiar tripartite proposal, languages like English generate (i) denoters of a basic type <e>; (ii) truth-evaluable sentences of a basic type <t>; and (iii) expressions of nonbasic types that are characterized recursively: if <A> and <B> are types, so is <A,B>; where expressions of type <A,B> signify functions, from things of the sort signified with expressions of type <A> to things of the sort signified with expressions of type <B>. On this view, human languages are importantly like the language that Frege invented to study the foundations of arithmetic. In this chapter it is argued that each third of the tripartite proposal is wrong. An alternative is then sketched according to which there are exactly two semantic types, corresponding to monadic and dyadic concepts.

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Mifflin, Houghton. Math Expressions Grade K Volume 1 (Teacher's Guide). Houghton Mifflin, 2006.

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Eureka Math, A Story of Ratios : Grade 7, Module 3: Expressions and Equations. Jossey-Bass, 2014.

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Частини книг з теми "ARITHMETIC EXPRESSION"

Weik, Martin H. "arithmetic expression." In Computer Science and Communications Dictionary, 62. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_822.

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Cseresnyes, Ehud, and Hannes Seiwert. "Regular Expression Length via Arithmetic Formula Complexity." In Descriptional Complexity of Formal Systems, 26–38. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-62536-8_3.

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Chivers, Ian. "Arithmetic and Expressions." In Essential C# fast, 55–88. London: Springer London, 2003. http://dx.doi.org/10.1007/978-1-4471-0075-1_4.

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Minato, Shin-ichi. "Arithmetic Boolean Expressions." In The Kluwer International Series in Engineering and Computer Science, 109–28. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-1303-8_9.

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Kulisch, Ulrich, Rolf Hammer, Matthias Hocks, and Dietmar Ratz. "Evaluation of Arithmetic Expressions." In C++ Toolbox for Verified Computing I, 140–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79651-7_8.

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Kulisch, Ulrich, Rolf Hammer, Dietmar Ratz, and Matthias Hocks. "Evaluation of Arithmetic Expressions." In Springer Series in Computational Mathematics, 131–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-78423-1_8.

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Lamprecht, Günther. "The Formation of Arithmetic Expressions." In Introduction to FORTRAN 77, 10–15. Wiesbaden: Vieweg+Teubner Verlag, 1986. http://dx.doi.org/10.1007/978-3-322-89421-2_3.

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Chemuturi, Murali. "Arithmetic, Relational, and Logical Expressions." In Computer Programming for Beginners, 61–72. Boca Raton : Taylor & Francis, 2019.: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9780429453250-7.

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Haase, Christoph, and Jakub Różycki. "On the Expressiveness of Büchi Arithmetic." In Lecture Notes in Computer Science, 310–23. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71995-1_16.

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AbstractWe show that the existential fragment of Büchi arithmetic is strictly less expressive than full Büchi arithmetic of any base, and moreover establish that its $$\varSigma _2$$ Σ 2 -fragment is already expressively complete. Furthermore, we show that regular languages of polynomial growth are definable in the existential fragment of Büchi arithmetic.

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Constantinides, George, Fredrik Dahlqvist, Zvonimir Rakamarić, and Rocco Salvia. "Rigorous Roundoff Error Analysis of Probabilistic Floating-Point Computations." In Computer Aided Verification, 626–50. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81688-9_29.

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AbstractWe present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are generally close to being uncorrelated with their generating distribution. Based on these theoretical advances, we propose a model of IEEE floating-point arithmetic for numerical expressions with probabilistic inputs and an algorithm for evaluating this model. Our algorithm provides rigorous bounds to the output and error distributions of arithmetic expressions over random variables, evaluated in the presence of roundoff errors. It keeps track of complex dependencies between random variables using an SMT solver, and is capable of providing sound but tight probabilistic bounds to roundoff errors using symbolic affine arithmetic. We implemented the algorithm in the PAF tool, and evaluated it on FPBench, a standard benchmark suite for the analysis of roundoff errors. Our evaluation shows that PAF computes tighter bounds than current state-of-the-art on almost all benchmarks.

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Тези доповідей конференцій з теми "ARITHMETIC EXPRESSION"

Liu, Xiahua, Chun Yang, and Zixin Guan. "Efficient arithmetic expression optimization with weighted adjoint matrix." In 2020 IEEE 39th International Performance Computing and Communications Conference (IPCCC). IEEE, 2020. http://dx.doi.org/10.1109/ipccc50635.2020.9391519.

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Pokorny, A., and J. Wolff von Gudenberg. "Expression Defined Accuracy." In 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006). IEEE, 2006. http://dx.doi.org/10.1109/scan.2006.17.

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Adamovich, Igor Alexeevich, and Yuri Andreevich Klimov. "Specialization of interpreters written in object-oriented languages can be effective." In 24th Scientific Conference “Scientific Services & Internet – 2022”. Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/abrau-2022-18.

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Barriers of real object-oriented program specialization can be often overcome using modern metacomputation techniques. One of the barriers is the resolution of polymorphism at the stage of program analysis before the 4 execution of the program. The last problem is successfully solved for a number of cases in the JaSpe specializer, as shown in this paper. The paper is devoted to the program compilation by specialization methods, without the use of a compiler. We have applied the partial evaluator JaSpe to two arithmetic expression language interpreters written in Java. The interpreters were implemented using the recursive descent method and the visitor pattern. As a result of the successful specialization of these interpreters by the square root program written on arithmetic expression language, compiled versions of the latter were obtained. In this case, the acceleration was from 12 to 22 times.

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Fakheri, Ahmad. "Thermal Efficiency of the Cross Flow Heat Exchangers." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-13575.

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The heat exchanger efficiency is defined as the ratio of the actual heat transfer in a heat exchanger to the optimum heat transfer rate. The optimum heat transfer rate, qopt, is given by the product of UA and the Arithmetic Mean Temperature Difference, which is the difference between the average temperatures of hot and cold fluids. The actual rate of heat transfer in a heat exchanger is always less than this optimum value, which takes place in an ideal balanced counter flow heat exchanger. It has been shown that for parallel flow, counter flow, and shell and tube heat exchanger the efficiency is only a function of a single nondimensional parameter called Fin Analogy Number. The function defining the efficiency of these heat exchangers is identical to that of a constant area fin with an insulated tip. This paper presents exact expressions for the efficiencies of the different cross flow heat exchangers. It is shown that by generalizing the definition of Fa, very accurate results can be obtained by using the same algebraic expression, or a single algebraic expression can be used to assess the performance of a variety of commonly used heat exchangers.

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Morgado Hernández, Cindy, and Gabriel Yáñez Canal. "Bayesian reasoning: connecting arithmetic, algebra and tree diagrams. A longitudinal research." In Advances in Statistics Education: Developments, Experiences, and Assessments. International Association for Statistical Education, 2015. http://dx.doi.org/10.52041/srap.15111.

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This paper shows some of the results of the research conducted with the purpose of knowing the Bayesian reasoning of college students doing their first course in probability and statistics. For this there three tests that were designed and implemented at different times during the semester. The results showed three stages in the reasoning of the students: the first, which coincides with the first test, is characterized by the use of mathematical arguments proportions; the second, which coincides with the second test is characterized by the joint use of tree diagrams and algebraic expression of Bayes which had been taught by teachers; the third, which coincides with the third test, is characterized by the failed recall Bayes rule and incomplete use of the tree diagram attempt.

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Jing, Yuxuan, and Rami M. Younis. "Cache-Aware and Roofline-Ideal Automatic Differentiation." In SPE Reservoir Simulation Conference. SPE, 2021. http://dx.doi.org/10.2118/203933-ms.

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Abstract Automatic differentiation software libraries augment arithmetic operations with their derivatives, thereby relieving the programmer of deriving, implementing, debugging, and maintaining derivative code. With this encapsulation however, the responsibility of code optimization relies more heavily on the AD system itself (as opposed to the programmer and the compiler). Moreover, given that there are multiple contexts in reservoir simulation software for which derivatives are required (e.g. property package and discrete operator evaluations), the AD infrastructure must also be adaptable. An Operator Overloading AD design is proposed and tested to provide scalability and computational efficiency seemlessly across memory- and compute-bound applications. This is achieved by 1) use of portable and standard programming language constructs (C++17 and OpenMP 4.5 standards), 2) adopting a vectorized programming interface, 3) lazy evaluation via expression templates, and 4) multiple memory alignment and layout policies. Empirical analysis is conducted on various kernels spanning various arithmetic intensity and working set sizes. Cache- aware roofline analysis results show that the performance and scalability attained are reliably ideal. In terms of floapting point operations executed per second, the performance of the AD system matches optimized hand-code. Finally, the implementation is benchmarked using the Automatically Differentiable Expression Templates Library (ADETL).

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Fakheri, Ahmad. "Arithmetic Mean Temperature Difference and the Concept of Heat Exchanger Efficiency." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47360.

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In this paper, it is shown that the Arithmetic Mean Temperature Difference, which is the difference between the average temperatures of hot and cold fluids, can be used instead of the Log Mean Temperature Difference (LMTD) in heat exchanger analysis. For a given value of AMTD, there exists an optimum heat transfer rate, Qopt, given by the product of UA and AMTD such that the rate of heat transfer in the heat exchanger is always less than this optimum value. The optimum heat transfer rate takes place in a balanced counter flow heat exchanger and by using this optimum rate of heat transfer, the concept of heat exchanger efficiency is introduced as the ratio of the actual to optimum heat transfer rate. A general algebraic expression as well as a chart is presented for the determination of the efficiency and therefore the rate of heat transfer for parallel flow, counter flow, single stream, as well as shell and tube heat exchangers with any number of shells and even number of tube passes per shell. In addition to being more intuitive, the use of AMTD and the heat exchanger efficiency allow the direct comparison of the different types of heat exchangers.

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Fakheri, Ahmad. "The Shell and Tube Heat Exchanger Efficiency and Its Relation to Effectiveness." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-41633.

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The heat exchanger efficiency is defined as the ratio of the actual heat transfer in a heat exchanger to the optimum heat transfer rate. The optimum heat transfer rate, qopt, is given by the product of UA and the Arithmetic Mean Temperature Difference, which is the difference between the average temperatures of hot and cold fluids. The actual rate of heat transfer in a heat exchanger is always less than this optimum value, which takes place in a balanced counter flow heat exchanger. It is shown that for parallel flow, counter flow, and shell and tube heat exchanger the efficiency is only a function of a single nondimensional parameter called Fin Analogy Number. Remarkably, the functional dependence of the efficiency of these heat exchangers on this parameter is identical to that of a constant area fin with an insulated tip. Also a general algebraic expression as well as a generalized chart is presented for the determination of the efficiency of shell and tube heat exchangers with any number of shells and even number of tube passes per shell, when the Number of Transfer Units (NTU) and the capacity ratio are known. Although this general expression is a function of the number of shells and another nondimensional group, it turns out to be almost independent of the number of shells over a wide range of practical interest. The same general expression is also applicable to parallel and counter flow heat exchangers.

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Hupkes, Dieuwke, and Willem Zuidema. "Visualisation and 'Diagnostic Classifiers' Reveal how Recurrent and Recursive Neural Networks Process Hierarchical Structure (Extended Abstract)." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/796.

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In this paper, we investigate how recurrent neural networks can learn and process languages with hierarchical, compositional semantics. To this end, we define the artificial task of processing nested arithmetic expressions, and study whether different types of neural networks can learn to compute their meaning. We find that simple recurrent networks cannot find a generalising solution to this task, but gated recurrent neural networks perform surprisingly well: networks learn to predict the outcome of the arithmetic expressions with high accuracy, although performance deteriorates somewhat with increasing length. We test multiple hypotheses on the information that is encoded and processed by the networks using a method called diagnostic classification. In this method, simple neural classifiers are used to test sequences of predictions about features of the hidden state representations at each time step. Our results indicate that the networks follow a strategy similar to our hypothesised ‘cumulative strategy’, which explains the high accuracy of the network on novel expressions, the generalisation to longer expressions than seen in training, and the mild deterioration with increasing length. This, in turn, shows that diagnostic classifiers can be a useful technique for opening up the black box of neural networks.

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Nagayama, Shinobu, Tsutomu Sasao, and Jon T. Butler. "Numeric Function Generators Using Piecewise Arithmetic Expressions." In 2011 IEEE 41st International Symposium on Multiple-Valued Logic (ISMVL). IEEE, 2011. http://dx.doi.org/10.1109/ismvl.2011.32.

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Nagayama, Shinobu, Tsutomu Sasao, and Jon T. Butler. Numeric Function Generators Using Piecewise Arithmetic Expressions. Fort Belvoir, VA: Defense Technical Information Center, May 2011. http://dx.doi.org/10.21236/ada547649.

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Baader, Franz. Concept Descriptions with Set Constraints and Cardinality Constraints. Technische Universität Dresden, 2017. http://dx.doi.org/10.25368/2022.232.

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We introduce a new description logic that extends the well-known logic ALCQ by allowing the statement of constraints on role successors that are more general than the qualified number restrictions of ALCQ. To formulate these constraints, we use the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA), in which one can express Boolean combinations of set constraints and numerical constraints on the cardinalities of sets. Though our new logic is considerably more expressive than ALCQ, we are able to show that the complexity of reasoning in it is the same as in ALCQ, both without and with TBoxes.

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