Journal articles: 'ARITHMETIC EXPRESSION'

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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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Li, Yan Mei, and Jing Min Wang. "The Short-Term Load Forecasting Model Based on Improved Gene Expression Programming Arithmetic." Advanced Materials Research 219-220 (March 2011): 1395–98. http://dx.doi.org/10.4028/www.scientific.net/amr.219-220.1395.

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Applying the improved gene expression programming arithmetic to optimization plan,the convergence rate and precision of the model can be improved,which can be used to load forecasting. Preprocessing the load sample data,and applying the flexible skills of the improved gene expression programming arithmetic ,the paper forecasts the whole point load of future short-term to see the same point load sequence of different work-day as sample.Through a case analysis,the improved gene expression programming arithmetic has been proved to have more efficiency and faster convergence rate than optimization methods.

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Das, Kaushik. "A Study on Misconception of Using Brackets in Arithmetic Expression." Shanlax International Journal of Education 8, no. 4 (September 1, 2020): 76–80. http://dx.doi.org/10.34293/education.v8i4.3252.

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The present study focused on the lack of knowledge of the double use of brackets in arithmetic expressions and the difficulty in the operatively of expression for mathematics application at the school level. Learning the other rules and formulas of mathematics involves learning the use of a bracket. Binding is useful in both arithmetic and algebra. If the bracket is not used properly, the value of the mathematical result is completely changed. The concept of this bracket is inserted into the students while learning school-based mathematics. So at the beginning of the bracket learning process, school-based textbooks, curriculum, and teachers are of great importance. The methodology of the proposed study is based on the document-based analysis. This study employed including studying international and national journals, library consultation, expert opinion, online journals, periodical, newspapers, and documents. Finally, the researcher suggested the importance, precaution, and effectiveness of using brackets in arithmetic.

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Wang, Ting, Hao Xun Tan, and Ren Ren Liu. "An Effective Conversion Algorithm of Arithmetic Expression from Infix Form to Prefix Form." Applied Mechanics and Materials 58-60 (June 2011): 1350–53. http://dx.doi.org/10.4028/www.scientific.net/amm.58-60.1350.

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Generally, when we optimize the object code of expression in source program, we get the optimizing code in the binary tree of this expression. Expressions in source program are in infix form, while the prefix form is more efficient for the binary tree. Hence this paper is to provide an effective transition algorithm of arithmetic expression from infix form to prefix form.

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PEYTON JONES, SIMON. "3 Expressions." Journal of Functional Programming 13, no. 1 (January 2003): 17–38. http://dx.doi.org/10.1017/s0956796803000510.

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3.1 Errors 193.2 Variables, Constructors, Operators, and Literals 203.3 Curried Applications and Lambda Abstractions 213.4 Operator Applications 213.5 Sections 223.6 Conditionals 233.7 Lists 233.8 Tuples 243.9 Unit Expressions and Parenthesized Expessions 253.10 Arithmetic Sequences 253.11 List Comprehensions 253.12 Let Expressions 273.13 Case Expressions 273.14 Do Expressions 293.15 Datatypes with Field Labels 293.16 Expression Type Signatures 323.17 Pattern Matching 32

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Demmel, James, Ioana Dumitriu, Olga Holtz, and Plamen Koev. "Accurate and efficient expression evaluation and linear algebra." Acta Numerica 17 (April 25, 2008): 87–145. http://dx.doi.org/10.1017/s0962492906350015.

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We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By ‘accurate’ we mean that the computed answer has relative error less than 1, i.e., has some correct leading digits. We also address efficiency, by which we mean algorithms that run in polynomial time in the size of the input. Our results will depend strongly on the model of arithmetic: most of our results will use the so-called traditional model (TM), where the computed result of op(a, b), a binary operation like a+b, is given by op(a, b) * (1+δ) where all we know is that |δ| ≤ ε ≪ 1. Here ε is a constant also known as machine epsilon.We will see a common reason for the following disparate problems to permit accurate and efficient algorithms using only the four basic arithmetic operations: finding the eigenvalues of a suitably discretized scalar elliptic PDE, finding eigenvalues of arbitrary products, inverses, or Schur complements of totally non-negative matrices (such as Cauchy and Vandermonde), and evaluating the Motzkin polynomial. Furthermore, in all these cases the high accuracy is ‘deserved’, i.e., the answer is determined much more accurately by the data than the conventional condition number would suggest.In contrast, we will see that evaluating even the simple polynomial x + y + z accurately is impossible in the TM, using only the basic arithmetic operations. We give a set of necessary and sufficient conditions to decide whether a high accuracy algorithm exists in the TM, and describe progress toward a decision procedure that will take any problem and provide either a high-accuracy algorithm or a proof that none exists.When no accurate algorithm exists in the TM, it is natural to extend the set of available accurate operations by a library of additional operations, such as x + y + z, dot products, or indeed any enumerable set which could then be used to build further accurate algorithms. We show how our accurate algorithms and decision procedure for finding them extend to this case.Finally, we address other models of arithmetic, and the relationship between (im)possibility in the TM and (in)efficient algorithms operating on numbers represented as bit strings.

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Yang, Guangjun, Xiaoling Yang, and Ping Wang. "Arithmetic-Analytic Representation of Peano Curve." International Journal of Mathematics and Mathematical Sciences 2019 (September 10, 2019): 1–7. http://dx.doi.org/10.1155/2019/6745202.

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In this work, we obtained a nonmatrix analytic expression for the generator of the Peano curve. Applying the iteration method of fractal, we established a simple arithmetic-analytic representation of the Peano curve as a function of ternary numbers. We proved that the curve passes each point in a unit square and that the coordinate functions satisfy a Hölder inequality with index α=1/2, which implies that the curve is everywhere continuous and nowhere differentiable.

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Wiener, Richard. "Arithmetic Function Interpreter in C# 3.0 Using Lambda Expression Trees." Journal of Object Technology 7, no. 3 (2008): 41. http://dx.doi.org/10.5381/jot.2008.7.3.c4.

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Gu, Yujie. "A Novel Inverse Credibility Distribution Approach for the Membership Functions of LRFuzzy Intervals: A Case Study on a Completion Time Analysis." Symmetry 14, no. 8 (July 28, 2022): 1554. http://dx.doi.org/10.3390/sym14081554.

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Fuzzy arithmetic is of great significance in dealing with vague information, especially the basic arithmetic operations (i.e., ⊕, ⊖, ⊗, ⊙). However, the classical and widely accepted accurate and approximate approaches, the interval arithmetic approach and standard approximation method, cannot output accurate or well-approximated expressions of the membership function, which may prevent decision makers from making the right decisions in real applications. To tackle this problem, this paper first discusses the relationships among the membership function, the credibility distribution, and the inverse credibility distribution and summarizes the relationships as several theorems. Then, by means of the theorems and the newly proposed operational law, this paper proposes an inverse credibility distribution approach that can output the accurate expression of the membership function for continuous and strictly monotone functions of regular LR fuzzy intervals. To better demonstrate the effectiveness of the raised approach, the commonly-used LR fuzzy interval, the symmetric trapezoidal fuzzy number, is employed, and several comparisons with the other two methods are made. The results show that the proposed approach can output an exact or well-approximated expression of the membership function, which the others cannot. In addition, some comparisons of the proposed approach with other methods are also made on a completion time analysis of a construction project to show the effectiveness of the proposed approach in real applications.

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McMullen, Jake, Kaisa Kanerva, Erno Lehtinen, Minna M. Hannula-Sormunen, and Noona Kiuru. "Adaptive number knowledge in secondary school students: Profiles and antecedents." Journal of Numerical Cognition 5, no. 3 (December 20, 2019): 283–300. http://dx.doi.org/10.5964/jnc.v5i3.201.

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The present study aims to examine inter-individual differences in adaptive number knowledge in secondary school students. Adaptive number knowledge is defined as a well-connected network of knowledge of numerical characteristics and arithmetic relations. Substantial and relevant qualitative differences in the strategies and expression of adaptive number knowledge have been found in primary school students still in the process of learning arithmetic. We present a study involving 879 seventh-grade students that examines the structure of individual differences in adaptive number knowledge with students who have completed one year of algebra instruction. Results of a latent profile analysis reveal a model that is similar than was previously found in primary school students. As well, arithmetic fluency and the development of arithmetic fluency are strong predictors of adaptive number knowledge latent profile membership. These results suggest that adaptive number knowledge may be characteristic of high-level performance extending into secondary school, even after formal instruction with arithmetic concludes.

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Lin, Chun-Ling, Melody Jung, Ying Choon Wu, Hsiao-Ching She, and Tzyy-Ping Jung. "Neural Correlates of Mathematical Problem Solving." International Journal of Neural Systems 25, no. 02 (February 12, 2015): 1550004. http://dx.doi.org/10.1142/s0129065715500045.

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This study explores electroencephalography (EEG) brain dynamics associated with mathematical problem solving. EEG and solution latencies (SLs) were recorded as 11 neurologically healthy volunteers worked on intellectually challenging math puzzles that involved combining four single-digit numbers through basic arithmetic operators (addition, subtraction, division, multiplication) to create an arithmetic expression equaling 24. Estimates of EEG spectral power were computed in three frequency bands — θ (4–7 Hz), α (8–13 Hz) and β (14–30 Hz) — over a widely distributed montage of scalp electrode sites. The magnitude of power estimates was found to change in a linear fashion with SLs — that is, relative to a base of power spectrum, theta power increased with longer SLs, while alpha and beta power tended to decrease. Further, the topographic distribution of spectral fluctuations was characterized by more pronounced asymmetries along the left–right and anterior–posterior axes for solutions that involved a longer search phase. These findings reveal for the first time the topography and dynamics of EEG spectral activities important for sustained solution search during arithmetical problem solving.

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Scrofano, Ronald, Ling Zhuo, and Viktor K. Prasanna. "Area-Efficient Arithmetic Expression Evaluation Using Deeply Pipelined Floating-Point Cores." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 16, no. 2 (February 2008): 167–76. http://dx.doi.org/10.1109/tvlsi.2007.912038.

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Grabowski, Tomasz, Jerzy Jan Jaroszewski, Shayne Cox Gad, and Marcin Feder. "Correlation Between In Silico Physicochemical Characteristics of Drugs and Their Mean Residence Time in Human and Dog." International Journal of Toxicology 31, no. 1 (January 2012): 25–33. http://dx.doi.org/10.1177/1091581811429865.

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The correlation between 52 physicochemical parameters and mean residence time (MRT) for 27 drugs used in human and dog were investigated. The physicochemical parameter values calculated provided a basis for deriving a series of arithmetic expressions, which were used to build a mathematical model describing the relationship between them and the MRT values. From the entire set of analyzed parameters, a subset of 14 was identified that contributed to the derivation of an arithmetic expression: [Formula: see text] the value of which is highly correlated with the MRT value in dogs ( P < .001) and allowed prediction of the MRT predicted (MRT(pred)). In humans, no correlation was found that allowed the calculation of MRT(pred). These results indicate that predicting the pharmacokinetics of any specific drug for humans based on pharmacokinetic data obtained in the dog should be undertaken with knowledge of the inherent limitations.

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Stone, R. T., and C. S. Wei. "Exploring the Linkage between Facial Expression and Mental Workload for Arithmetic Tasks." Proceedings of the Human Factors and Ergonomics Society Annual Meeting 55, no. 1 (September 1, 2011): 616–19. http://dx.doi.org/10.1177/1071181311551126.

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Yang, Xiao-ling, and Guang-jun Yang. "Arithmetic-analytical expression of the Koch-type curves and their generalizations (I)." Acta Mathematicae Applicatae Sinica, English Series 31, no. 4 (October 2015): 1167–80. http://dx.doi.org/10.1007/s10255-015-0522-0.

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Madigan, Michael F., J. Alexander Dale, and Jeffrey D. Cross. "No Respite during Sleep: Heart-Rate Hyperreactivity to Rapid Eye Movement Sleep in Angry Men Classified as Type A." Perceptual and Motor Skills 85, no. 3_suppl (December 1997): 1451–54. http://dx.doi.org/10.2466/pms.1997.85.3f.1451.

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9 men scoring as Type A and Angry and 9 men scoring as Type B and Nonangry on the Jenkins Activity Survey and Spielberger's Trait Anger Expression completed a 1-min. mental arithmetic task and slept through 1 period of rapid eye movement. The Angry Type A scorers showed greater heart-rate increases from baseline to that during mental arithmetic and from nonrapid eye movements to periods of REM than the Nonangry Type B scorers. While the former showed equivalent reactivity to stressors while awake and asleep, the latter group showed less heart-rate reactivity during the period of REM than during mental arithmetic. Neither group yielded clear descriptions of their dreams, and no differences between groups were noted for ratings on aggressivity in dreams. It appears that Angry Type A scorers show cardiovascular hyperreactivity even when asleep in the lab.

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Patil, Abhiruchi, and Teena Varma. "Handwritten Mathematical Expression Solver using CNN." International Journal for Research in Applied Science and Engineering Technology 10, no. 9 (September 30, 2022): 1205–10. http://dx.doi.org/10.22214/ijraset.2022.46803.

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Abstract: Mathematics is the universal language. It is the core of all the scientific discoveries and is used extensively in all possible fields. Hence, there arises the need for fast computation and instant results. This has led to the development of various technologies and machines which would ease the strain on humans and also reduce the error and delays caused by them. Our project caters to these needs by reducing the effort on user side. We want to make the experience of experimenting with equations as simple as possible. The application is capable of performing fast calculations on human handwritten mathematical expressions. Basic calculations like arithmetic and trigonometric functions can be done along with simultaneous equations. The expression is extracted from the image and each character, symbol and number is recognised and then the entire expression is further being solved displaying all possible solutions. The application developed is simple and user-friendly tool that can leverage the power of existing powerful math packages.

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Kinoshita, C. M. "A Theoretical Analysis of Predrying of Solid Fuels With Flue Gas." Journal of Energy Resources Technology 110, no. 2 (June 1, 1988): 119–23. http://dx.doi.org/10.1115/1.3231365.

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Combustion efficiency and flue-gas drying of solid fuels are analyzed. A simple, universal arithmetic expression for combustion efficiency is developed. This expression involves four primary dimensionless parameters which relate to (and are fixed for given) fuel and ambient conditions, and three secondary dimensionless parameters which relate to (and vary with) fuel moisture content, excess air, and flue-gas temperature. Additional expressions involving the same primary parameters are developed to calculate the decrease in fuel moisture content due to flue-gas drying with and without entrainment of air into the dryer system and the decrease in flue-gas temperature with air entrainment. Values for the four primary parameters are presented for various fuels; their values do not vary much for most biomass fuels.

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Nehmeier, Marco. "Interval arithmetic using expression templates, template meta programming and the upcoming C++ standard." Computing 94, no. 2-4 (November 29, 2011): 215–28. http://dx.doi.org/10.1007/s00607-011-0176-6.

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Islam, S. M. S., A. K. Z. Ahmed, H. Gunarto, and A. A. K. Majumdar. "A Unified Approach to the Sandor-Smarandache Function." Journal of Scientific Research 14, no. 3 (September 1, 2022): 699–720. http://dx.doi.org/10.3329/jsr.v14i3.56205.

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The Sandor-Smarandache function, SS(n), is a recently introduced Smarandache-type arithmetic function, which involves binomial coefficients. It is known that SS(n) does not possess many of the common properties of the classical arithmetic functions of the theory of numbers. Sandor gave the expression of SS(n) when n ( ³ 3) is an odd integer. It is found that SS(n) has a simple form when n is even and not divisible by 3. In the previous papers, some closed-form expressions of SS(n) have been derived for some particular cases of n. This paper continues to find more forms of SS(n), starting from the function SS(24m). Particular attention is given to finding necessary and sufficient conditions such that SS(n) = n–5 and SS(n) = n–6. Based on the properties of SS(n), some interesting Diophantine equations have been studied. The study reveals that the form of SS(n) depends on the prime factors of the integer n in the natural order of the primes.

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Kobayashi, Mitsuo. "A generalization of a series for the density of abundant numbers." International Journal of Number Theory 12, no. 03 (March 23, 2016): 671–77. http://dx.doi.org/10.1142/s1793042116500445.

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Recently, it was shown that the density of abundant numbers has a simple series expression, which relies on the multiplicative property of the arithmetic function [Formula: see text]. We generalize this result by determining a class of multiplicative functions for which the series result carries over.

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Zhang, Liyuan. "Progress and Emotion Expression of Campus Cultural Innovation Goods Based on Data Mining under Culture Shock Environment." Journal of Environmental and Public Health 2022 (September 12, 2022): 1–9. http://dx.doi.org/10.1155/2022/4874748.

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With the rapid progress of economy and globalization, the characteristic culture of universities is inevitably eroded by the strong mainstream culture from outside. The best way to maintain culture is to turn it into goods. Productization can make culture vivid and vivid and circulate in use. Universities are the carrier of education and the progress of excellent culture. Campus culture refers to all tangible and intangible objective existence created artificially and formed for a long time in a specific school environment, which can deeply reflect the characteristics of the school. This article proposes an optimized design scheme for the progress and emotional expression research of campus cultural innovative goods in universities. It constructs the graphics recognition of campus cultural goods through the data mining system and then focuses on the problem of graphics recognition based on DL (deep learning). An enhanced DL model and arithmetic are proposed to enhance the accuracy and efficiency of graphics recognition. Finally, the simulation test and analysis are carried out. The simulation results show that the proposed arithmetic has certain accuracy, which is 10.23% higher than the traditional DL arithmetic. Campus culture can also play a powerful role in emotional edification and personality shaping for teachers, students, and campus workers. Excellent cultural and innovative goods can inherit the history, culture, and spirit of universities and can directly reflect the cultural heritage, characteristics, and graphics of universities. In addition to promoting the precipitation and inheritance of the long history and culture of universities and the spirit of the times, they can also strengthen the cultural exchange and spiritual communication among college level, alumni, teachers, and students, and people from all walks of life in universities, so as to actively promote the cultural and spiritual construction of universities.

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Stanimirovic, Predrag, Predrag Krtolica, and Rade Stanojevic. "A non-recursive algorithm for polygon triangulation." Yugoslav Journal of Operations Research 13, no. 1 (2003): 61–67. http://dx.doi.org/10.2298/yjor0301061s.

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In this paper an algorithm for the convex polygon triangulation based on the reverse Polish notation is proposed. The formal grammar method is used as the starting point in the investigation. This idea is "translated" to the arithmetic expression field enabling application of the reverse Polish notation method. .

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KUROKAWA, NOBUSHIGE, MASATO WAKAYAMA, and YOSHINORI YAMASAKI. "RUELLE TYPE L-FUNCTIONS VERSUS DETERMINANTS OF LAPLACIANS FOR TORSION FREE ABELIAN GROUPS." International Journal of Mathematics 19, no. 08 (September 2008): 957–79. http://dx.doi.org/10.1142/s0129167x08004959.

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We study Ruelle's type zeta and L-functions for a torsion free abelian group Γ of rank ν ≥ 2 defined via an Euler product. It is shown that the imaginary axis is a natural boundary of this zeta function when ν = 2, 4 and 8, and in particular, such a zeta function has no determinant expression. Thus, conversely, expressions like Euler's product for the determinant of the Laplacians of the torus ℝν/Γ defined via zeta regularizations are investigated. Also, the limit behavior of an arithmetic function arising from the Ruelle type zeta function is observed.

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Yang, Xiaoling, and Ying Tan. "An Arithmetic-Analytical Expression of the Hilbert-Type Space-Filling Curves and Its Applications." Bulletin of the Malaysian Mathematical Sciences Society 38, no. 2 (November 19, 2014): 841–54. http://dx.doi.org/10.1007/s40840-014-0052-6.

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Chow, Yuen Ler, Shantanu Singh, Anne E. Carpenter, and Gregory P. Way. "Predicting drug polypharmacology from cell morphology readouts using variational autoencoder latent space arithmetic." PLOS Computational Biology 18, no. 2 (February 25, 2022): e1009888. http://dx.doi.org/10.1371/journal.pcbi.1009888.

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A variational autoencoder (VAE) is a machine learning algorithm, useful for generating a compressed and interpretable latent space. These representations have been generated from various biomedical data types and can be used to produce realistic-looking simulated data. However, standard vanilla VAEs suffer from entangled and uninformative latent spaces, which can be mitigated using other types of VAEs such as β-VAE and MMD-VAE. In this project, we evaluated the ability of VAEs to learn cell morphology characteristics derived from cell images. We trained and evaluated these three VAE variants—Vanilla VAE, β-VAE, and MMD-VAE—on cell morphology readouts and explored the generative capacity of each model to predict compound polypharmacology (the interactions of a drug with more than one target) using an approach called latent space arithmetic (LSA). To test the generalizability of the strategy, we also trained these VAEs using gene expression data of the same compound perturbations and found that gene expression provides complementary information. We found that the β-VAE and MMD-VAE disentangle morphology signals and reveal a more interpretable latent space. We reliably simulated morphology and gene expression readouts from certain compounds thereby predicting cell states perturbed with compounds of known polypharmacology. Inferring cell state for specific drug mechanisms could aid researchers in developing and identifying targeted therapeutics and categorizing off-target effects in the future.

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Hameed, Mustafa I., and Buthyna Najad Shihab. "Some Classes of Univalent Function with Negative Coefficients." Journal of Physics: Conference Series 2322, no. 1 (August 1, 2022): 012048. http://dx.doi.org/10.1088/1742-6596/2322/1/012048.

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Abstract The 𝛶 subclasses S*(τ, λ) and C*(τ, λ), as well as the class of analytic and univalent functions of the form h ( w ) = w − ∑ i = 2 ∞ | e i | w i , were studied. Sharp coefficients, distortion, as well as a function expression formula in S*(τ, λ) are determined, as well as expression formulae for functions in C*(τ, λ). In addition, convex linear combination over arithmetic average, the classes S*(τ, λ) and C*(τ, λ) are proved to be closed.

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Mercer, Joseph. "What Is Left to Teach If Students Can Use Calculators?" Mathematics Teacher 85, no. 6 (September 1992): 415–17. http://dx.doi.org/10.5951/mt.85.6.0415.

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Let us begin at the beginning, say. first grade. We give every student a simple calculator that does all the basic arithmetic operations, including square roots and operations with fractions, We teach every student to use the calculator, that is, to find the answer to problems like 2 + 5, 3 – 7, −4 + 9 – (−8), 32.97 × 485.47, 2/3 + 3/4, and so on. Students do not have to memorize anything except how to use the calculator to find the value of an arithmetic expression. Of course, they have to know how to read and write the numbers and know which keys denote plus, minus, and so on, so as to be able to communicate verbally with the teacher or someone else, so some learning is necessary besides pressing keys. But then what?

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ULAS, MACIEJ. "ARITHMETIC PROPERTIES OF THE SEQUENCE OF DEGREES OF STERN POLYNOMIALS AND RELATED RESULTS." International Journal of Number Theory 08, no. 03 (April 7, 2012): 669–87. http://dx.doi.org/10.1142/s1793042112500388.

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Let Bn(t) be an nth Stern polynomial and let e(n) = deg Bn(t) be its degree. In this note we continue our study started in [On certain arithmetic properties of Stern polynonials, Publ. Math. Debrecen79(1–2) (2011) 55–81] of the arithmetic properties of the sequence of Stern polynomials and the sequence [Formula: see text]. We also study the sequence d(n) = ord t=0 Bn(t). Among other things we prove that d(n) = ν(n), where ν(n) is the maximal power of 2 which divides the number n. We also count the number of the solutions of the equations e(m) = i and e(m) - d(m) = i in the interval [1, 2n]. We also obtain an interesting closed expression for a certain sum involving Stern polynomials.

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Bandyopadhyay, Baishali, Veda Chanda, and Yupeng Wang. "xSyn: A Software Tool for Identifying Sophisticated 3-Way Interactions From Cancer Expression Data." Cancer Informatics 16 (January 1, 2017): 117693511772851. http://dx.doi.org/10.1177/1176935117728516.

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Background: Constructing gene co-expression networks from cancer expression data is important for investigating the genetic mechanisms underlying cancer. However, correlation coefficients or linear regression models are not able to model sophisticated relationships among gene expression profiles. Here, we address the 3-way interaction that 2 genes’ expression levels are clustered in different space locations under the control of a third gene’s expression levels. Results: We present xSyn, a software tool for identifying such 3-way interactions from cancer gene expression data based on an optimization procedure involving the usage of UPGMA (Unweighted Pair Group Method with Arithmetic Mean) and synergy. The effectiveness is demonstrated by application to 2 real gene expression data sets. Conclusions: xSyn is a useful tool for decoding the complex relationships among gene expression profiles. xSyn is available at http://www.bdxconsult.com/xSyn.html .

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Ortner, Michael, Peter Leitner, and Florian Slanovc. "Numerically Stable and Computationally Efficient Expression for the Magnetic Field of a Current Loop." Magnetism 3, no. 1 (December 30, 2022): 11–31. http://dx.doi.org/10.3390/magnetism3010002.

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In this work, it is demonstrated that straightforward implementations of the well-known textbook expressions of the off-axis magnetic field of a current loop are numerically unstable in a large region of interest. Specifically, close to the axis of symmetry and at large distances from the loop, complete loss of accuracy happens surprisingly fast. The origin of the instability is catastrophic numerical cancellation, which cannot be avoided with algebraic transformations. All exact expressions found in the literature exhibit similar instabilities. We propose a novel exact analytic expression, based on Bulirsch’s complete elliptic integral, which is numerically stable (15–16 significant figures in 64 bit floating point arithmetic) everywhere. Several field approximation methods (dipole, Taylor expansions, Binomial series) are studied in comparison with respect to accuracy, numerical stability and computation performance. In addition to its accuracy and global validity, the proposed method outperforms the classical solution, and even most approximation schemes in terms of computational efficiency.

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Rao, Ganti Prasada, and Darwish M. K. Al-Gobaisi. "A Pattern of Expression from Indo-Arabic Arithmetic to the Mathematics of Signals and Systems." IETE Journal of Education 34, no. 1 (January 1993): 59–65. http://dx.doi.org/10.1080/09747338.1993.11436400.

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Tent, Margaret W. "Understanding the Properties of Arithmetic: A Prerequisite for Success in Algebra." Mathematics Teaching in the Middle School 12, no. 1 (August 2006): 22–25. http://dx.doi.org/10.5951/mtms.12.1.0022.

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As early as fourth grade, we begin introducing students to the properties of arithmetic. The commutative property of addition and the commutative property of multiplication allow us to change the order of the numbers without changing the value of the expression. The associative property of addition and the associative property of multiplication state that regrouping numbers when adding and/or multiplying does not change the solution. The distributive property of multiplication over addition allows us either to find the addend of the numbers, then multiply by the factor, or to first multiply the factor by each addend, then find the sum. Finally, the identity properties of addition and multiplication state that the value of any real number remains unchanged if zero is added to it or if it is multiplied by one, respectively.

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Roy, Subhro, and Dan Roth. "Mapping to Declarative Knowledge for Word Problem Solving." Transactions of the Association for Computational Linguistics 6 (December 2018): 159–72. http://dx.doi.org/10.1162/tacl_a_00012.

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Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several mathematical concepts such as dimensional analysis, subset relationships, etc. In this paper, we develop declarative rules which govern the translation of natural language description of these concepts to math expressions. We then present a framework for incorporating such declarative knowledge into word problem solving. Our method learns to map arithmetic word problem text to math expressions, by learning to select the relevant declarative knowledge for each operation of the solution expression. This provides a way to handle multiple concepts in the same problem while, at the same time, supporting interpretability of the answer expression. Our method models the mapping to declarative knowledge as a latent variable, thus removing the need for expensive annotations. Experimental evaluation suggests that our domain knowledge based solver outperforms all other systems, and that it generalizes better in the realistic case where the training data it is exposed to is biased in a different way than the test data.

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Zhao, Yiqian. "An Evaluation Model for the Influence Factors of Interest in Literature Courses Based on Data Analysis and Association Rules in a Small-Sample Environment." Journal of Environmental and Public Health 2022 (September 9, 2022): 1–9. http://dx.doi.org/10.1155/2022/1900509.

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The primary tools for developing pupils’ creativity, capacity for verbal expression, and spiritual growth are literary reading and writing. Literature is a sort of art that elicits feelings and expresses the author’s comprehension and outlook on social life via the use of language. Reading and writing literary works helps students develop their aesthetic sensibilities and capacity to create compelling images, as well as their spirituality and wisdom. This study suggests a data mining-based optimal design approach for analyzing association rules of influencing aspects of interest in literary courses. To increase the frequency and accuracy of data mining, association rules are used to obtain the association mapping relationship between data sets of influencing factors of interest in literature courses. Rough set theory is then used to distinguish between the feature sets of data sets in the same subspace and different subspaces. To identify the most prevalent factor that affects the interest of the curriculum’s literary components and then to conduct simulation testing and analysis. The proposed arithmetic has a particular accuracy, which is 8.25% greater than the conventional arithmetic, according to simulation findings. This outcome demonstrates in full how the enhanced arithmetic decreases the amount of records in the scanning database by grouping and compressing the database, hence lowering the scanning time and pruning before the connection process of Liu arithmetic. Classical literary works are without a doubt the most valuable resources to feed, edify, forge, and grow the spirit, soul, and personality of contemporary individuals throughout history and in all nations. Education through literature develops one’s character, spirit, emotions, and aesthetic sense. The importance of reaffirming the significant place of literature education in contemporary national basic education cannot be overstated.

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Zhu, Chuanlin, Yuhan Jiang, Yun Wang, Dianzhi Liu, and Wenbo Luo. "Arithmetic performance is modulated by cognitive reappraisal and expression suppression: Evidence from behavioral and ERP findings." Neuropsychologia 162 (November 2021): 108060. http://dx.doi.org/10.1016/j.neuropsychologia.2021.108060.

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Gutman, Ivan, Gopalapillai Indulal, and Roberto Todeschinic. "Generalizing the McClelland Bounds for Total π-Electron Energy." Zeitschrift für Naturforschung A 63, no. 5-6 (June 1, 2008): 280–82. http://dx.doi.org/10.1515/zna-2008-5-607.

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In 1971 McClelland obtained lower and upper bounds for the total π-electron energy. We now formulate the generalized version of these bounds, applicable to the energy-like expression EX = Σni =1 |xi − x̅|, where x1,x2, . . . ,xn are any real numbers, and x̅ is their arithmetic mean. In particular, if x1,x2, . . . ,xn are the eigenvalues of the adjacency, Laplacian, or distance matrix of some graph G, then EX is the graph energy, Laplacian energy, or distance energy, respectively, of G.

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Luebke, Jerry, Michael H. Epstein, and Douglas Cullinan. "Comparison of Teacher-Rated Achievement Levels of Behaviorally Disordered, Learning Disabled, and Nonhandicapped Adolescents." Behavioral Disorders 15, no. 1 (November 1989): 1–8. http://dx.doi.org/10.1177/019874298901500105.

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Teachers rated the achievement levels of behaviorally disordered, learning disabled, and nonhandicapped adolescents in four different academic areas: reading recognition, reading comprehension, arithmetic, and written expression. Comparisons across the three groups revealed that behaviorally disordered and learning disabled adolescents were seen as performing significantly below expected levels of achievement. Differences found between behaviorally disordered and learning disabled students' rated achievement appeared to depend upon particular age levels. Results are discussed in terms of the instructional needs of behaviorally disordered and learning disabled students.

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Talbert, Martha Kay, and Virginia Stallings-Roberts. "Introducing Prealgebra Skills in an Egg-citing Way." Mathematics Teaching in the Middle School 1, no. 3 (November 1994): 198–202. http://dx.doi.org/10.5951/mtms.1.3.0198.

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Like most teachers, the authors would frequently meet between classes and during office hours to plan and bounce teaching ideas off of each other. One day we were bemoaning the fact that some students could not seem to understand what a variable was, much less manipulate algebraic expressions. The discussion was a familiar one. Troubled students would magically transform the expression 2x + x to 2x2. Or these same beleaguered souls would decide that the easiest way to deal with substitution is to ignore it. While we were pondeting ways in which we could reach students, one of us excitedly pointed out that algebra is hidden arithmetic! It was then that the idea of eggalgebra began to unfold. The activity was primarily designed to help students understand the concept of a variable and the process of gathering like terms or simplifying algebraic expressions. We have found that students across many grade levels have appreciated and gained from working with egg-algebra.

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Khudjaev, Mukhiddin. "Analytical solution to the problem of fluid outflow from an axisymmetric channel." E3S Web of Conferences 371 (2023): 06004. http://dx.doi.org/10.1051/e3sconf/202337106004.

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The subject of the study is the outflow of fluid from a channel consisting of segments with different geometries used to improve thermal and hydraulic characteristics. Research methods are based on Newton's rheological law; the continuity equation and the Navier-Stokes equation, which are the basic equations of fluid flow; the method of mathematical modeling and the analytical method of its solutions. In the article, generalized formulas for determining the hydrodynamic characteristics of a fluid flow in axisymmetric channels are obtained. As an example, analytical expressions for the pressure and average flow velocity are obtained when fluid flows out of a cylindrical channel of a constant cross section and from a channel of a hyperbolic form. In perspective, by introducing an arbitrary arithmetic expression of the axisymmetric section of the channel, it is possible to determine the hydrodynamic characteristics of the flow.

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Khudjaev, Mukhiddin. "Simulation of fluid outflow from an axisymmetric channel." E3S Web of Conferences 390 (2023): 04033. http://dx.doi.org/10.1051/e3sconf/202339004033.

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The subject of the study is the outflow of fluid from a channel consisting of segments with different geometries used to improve thermal and hydraulic characteristics. Research methods are based on Newton's rheological law; the continuity equation and the Navier-Stokes equation, which are the basic equations of fluid flow; the method of mathematical modeling and the analytical method of its solutions. In the article, generalized formulas for determining the hydrodynamic characteristics of a fluid flow in axisymmetric channels are obtained. As an example, analytical expressions for the pressure and average flow velocity are obtained when fluid flows out of a cylindrical channel of a constant cross section and from a channel of a hyperbolic form. In perspective, by introducing an arbitrary arithmetic expression of the axisymmetric section of the channel, it is possible to determine the hydrodynamic characteristics of the flow.

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Journal articles on the topic 'ARITHMETIC EXPRESSION'

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