Showing papers on "Decimal published in 2020"

Analysis of arithmetic for mathematics teaching

Abstract: Contents: Preface. J.T. Sowder, Making Sense of Numbers in School Mathematics. K.C. Fuson, Research on Learning and Teaching Addition and Subtraction of Whole Numbers. P. Nesher, Solving Multiplication Word Problems. M. Lampert, Teaching and Learning Long Division for Understanding in School. J. Hiebert, Mathematical, Cognitive, and Instructional Analyses of Decimal Fractions. T.E. Kieren, Rational and Fractional Numbers as Mathematical and Personal Knowledge: Implications for Curriculum and Instruction. L.B. Resnick, From Protoquantities to Operators: Building Mathematical Competence on a Foundation of Everyday Knowledge. M. Rauth, L. Billups, Epilogue.

Secure 3D data hiding technique based on a mesh traversal algorithm

Abstract: Due to its powerful ability to conceal secret data inside an unsuspicious cover object, image steganography has emerged as an active field of research. Recently, a lot of advancements in relation to software and hardware have been carried out, allowing for faster processing of 3D image models. In turn, this has paved the way for 3D image steganography. This paper proposes a novel approach of secure and reversible data hiding in 3D mesh models. The proposed approach employs a mesh traversal algorithm that is based on the shortest distances between neighboring vertices of the mesh. The fourth and fifth decimal places of the Cartesian coordinate vertices after the decimal point are modified to hide the secret data. The proposed approach is evaluated in terms of a number of metrics and is shown to outperform its counterparts from the literature.

Testing the application of corrective adjustment procedures for removal of relative age effects in female youth swimming

Abstract: The purpose of this study was (1) accurately estimate longitudinal relationships between decimal age (i.e., chronological and relative) and performance in Australian female 100 m (N = 765) and 200 ...

1 Slash 100%: gamification of mathematics with hybrid QR-based card game

Abstract: Mathematics is vital in our life and society. However, gamification of mathematics is rare for topics such as fractions and decimals. This paper presents the development of an educational mathematics game called one slash one hundred percent (1 Slash 100%). It is the hybridization of the conventional card game and quick response (QR). This research aims to study how the respondents explore the card game to master decimal, fraction and percentage. The testing was conducted among secondary school students in Kuching, Sarawak, Malaysia (n=12; age=14). The respondents were asked to answer a set of questions in pre-test and post-test question. The results are promising where the analysis showed a significant difference between pre-test (M=14.3, SD=2.103) and post-test scores (M=17.6, SD=2.234). Thus, gamification of mathematics using the hybrid card game increases their mastery of decimal, fraction and percentage.

The Sleep of Reason Produces Monsters: How and When Biased Input Shapes Mathematics Learning

Abstract: Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by ...

Fast signed multiplier using Vedic Nikhilam algorithm

Abstract: Vedic algorithm is beneficial for the application in the design of high-speed computing and hardware. This study presents a fast signed binary multiplication structure based on Vedic Nikhilam algorithm. The authors explored the Nikhilam sutra for unsigned decimal numbers to both signed decimal and binary operands. The proposed multiplier leads to significant gains in speed by converting a large operand multiplication to small operand multiplication, along with addition. The proposed design is synthesised with Xilinx ISE 14.4 software and realised using different field programmable gate array devices. The efficiency of the proposed design depends on combinational delay, area and power. Moreover, the new multiplier architecture achieves speed improvement over prior design.

On the algebraicity of Thue-Morse and period-doubling continued fractions

Abstract: We put forward several general conjectures concerning the algebraicity or transcendence of continued fractions and Stieltjes continued fractions defined by the Thue-Morse and period-doubling sequences in characteristic $2$ We present our Guess'n'Prove method, in which we exploit the structure of automata, for proving some of our conjectures in special cases

Curious convergent series of integers with missing digits

Abstract: A classical theorem of Kempner states that the sum of the reciprocals of positive integers with missing decimal digits converges. This result is extended to much larger families of "missing digits" sets of positive integers with both convergent and divergent harmonic series.

The 8th Grade Students' Competencies in Alternating Different Symbolic Representations of Rational Numbers.

Abstract: One of the attributes of rational numbers that make them different from integers are the different symbolic modes (fraction, decimal and percentage) to which an identical number can be attributed (e.g. 1/4, 0.25 and 25%). Some research has identified students’ difficulty in mental calculations with rational numbers as has also the switching to different symbolic representations between fractions and decimals. However, pupils’ performance, and repertoire of strategies have not been systematically studied in mental calculations with rational numbers expressed in different symbolic representations. The principal question of this research: how is the ability of students to perform mental calculations with rational numbers affected when the same number changes in fraction, decimal and percentage? For the purpose of the study 62 8th grade students were interviewed to examine how this symbolic shift in the number of operations affects the success and type of strategies they use, and the ability to alternate the rotation of these symbolisms. The results of the research show that the symbolic change of the rational numbers affects the success and the type of strategies that students use in mental calculations. Another result of the study demonstrated that students are not flexible when switching between the different symbolic representations of rational numbers as benchmark while performing mental calculations.

A recurring pattern in natural numbers of a certain property

Abstract: Natural numbers satisfying an unusual property are mentioned by the author in [5], in which their infinitude is also proved. In this paper, we start with an arbitrary natural number which is not a multiple of 10 and non-palindromic, form numbers by concatenating its decimal digits, and investigate which of them have the unusual property. In particular, the pattern of which of them have the unusual property recurs.

Students' Strategy in Connecting Fractions, Decimal, and Percent in Solving Visual Form Problems

Abstract: Fractions, decimals, and percentages are a rational number that is very important in mathematics and everyday life. However, there are still many students experiencing difficulties in understanding the concept due to its complexity in the scope of application and technical. Difficulty in understanding fractions and decimals will undoubtedly have implication for learning. This study aims to describe visual problem-solving strategies related to rational numbers of junior high school students in solving visual form problems. Descriptive research with a mixed approach was used for this purpose, with 32 students of grade VII in the middle school consisting of 10 (31.25%) boys, and 22 (68.75%) girls were used as research subjects. Data obtained through the subject has written answers to four questions in the form of visuals, namely one question determines the fraction, decimal, and percent values of a shaded area and three questions make up an area if a fraction, decimal, and percent value is given and the relationships among of them, which are then analyzed descriptively. The analysis results show that the subject's strategy of connecting fractions, decimals, and percent using conceptual and arithmetic operations, has not utilized the visual images provided optimally. On the other hand, the visual model is very important in understanding abstract mathematical concepts. Thus, the use of multiple visuals in learning fractions, decimals, and percent should be a concern to the teacher, especially on the topic of fractions.

Parallelizing multiple precision Taylor series method for integrating the Lorenz system.

Abstract: A hybrid MPI+OpenMP strategy for parallelizing multiple precision Taylor series method is proposed, realized and tested. To parallelize the algorithm we combine MPI and OpenMP parallel technologies together with GMP library (GNU miltiple precision libary) and the tiny MPIGMP library. The details of the parallelization are explained on the paradigmatic model of the Lorenz system. We succeed to obtain a correct reference solution in the rather long time interval - [0,7000]. The solution is verified by comparing the results for 2700-th order Taylor series method and precision of ~ 3374 decimal digits, and those with 2800-th order and precision of ~ 3510 decimal digits. With 192 CPU cores in Nestum cluster, Sofia, Bulgaria, the 2800-th order computation was ~ 145 hours with speedup ~ 105.

Formação inicial de professores que ensinam matemática e o sistema de numeração decimal

Abstract: This article presents part of an ongoing doctoral research that uses the theoretical and methodological support of the Anthropological Theory of Didactics to question and answer whether the decimal numbering system is a naturalized knowledge within the practices of a group of teachers in initial training for students initial years of middle school The interest in this issue arises from the naturalization of decimals numbers, since there are difficulties in teaching and learning as objects structured according to the positional numbering system The methodology used, in line with the theoretical resources, was the development of a study and research path, based on a non-routine situation among school teaching practices in the initial grades, with the help of a study director taken among the authors of this research The results found confirm the initial hypothesis of naturalization of this numbering system by teachers in initial training and demonstrate and ratify the power of the methodology employed in this research as a teaching device, including for teacher training

LSTM Network and OCR Performance for Classification of Decimal Dewey Classification Code

Abstract: Background of the study: Giving book code by a librarian in accordance with the Decimal Dewey Classification system aims to facilitate the search for books on the shelf precisely and quickly. Purpose: The first step in giving code to determine the class of books is the principal division which has 10 classes. Method: This study proposed Optical Character Recognition to read the title text on the book cover, preprocessing the text, and classifying it by Long Short-Term Memory Neural Network. Findings: In general, a librarian labeled a book by reading the book title on the book cover and doing book class matching with the book guide of DDC. Automatically, the task requires time increasingly. We tried to classify the text without OCR and utilize OCR which functions to convert the text in images into text that is editable. BY the experimental result, the level of classification accuracy without utilizing OCR is higher than using OCR. Conclusion : The magnitude of the accuracy is 88.57% and 74.28% respectively. However, the participation of OCR in this classification is quite efficient enough to assist a beginner librarian to overcome this problem because the accuracy difference is less than 15%.

All-optical decimal to ternary converter with the proper use of optical non-linear material

Abstract: An all-optical system to convert the decimal number to ternary number is proposed here with the proper use of switching mechanism of Kerr-type optical nonlinear material. In this scheme the intensity level I, 2I, 3I, 4I, respectively, represents the decimal number 1, 2, 3, 4 which is used as the input bit. The output of the optical ternary state is represented by the absence of light (0), the presence of light with intensity level I (1) and the light of 2I intensity [1 bar ($$\overline{1}$$)]. Beam splitter and beam combiner are used here to maintain the desire intensity level.

Using of Redundant Signed-Digit Numeral System for Accelerating and Improving the Accuracy of Computer Floating-Point Calculations

Abstract: The article proposes a method for software implementation of floating-point computations on a graphics processing unit (GPU) with an increased accuracy, which eliminates sharp increase in rounding errors when performing arithmetic operations of addition, subtraction or multiplication with numbers that are significantly different from each other in magnitude. The method is based on the representation of floating-point numbers in the form of decimal fractions that have uniform distribution within a range and the use of redundant signed-digit numeral system to speed up calculations. The results of computational experiments for evaluating the effectiveness of the proposed approach are presented. The effect of accelerating computations is obtained for the problems of calculating the sum of an array of numbers and determining the dot product of vectors. The proposed approach is also applicable to the discrete Fourier transform.

From the history of the binary number system. thomas harriot

Abstract: For the first time in the Russian-language literature, the article analyzes the works of the English mathematician, geographer and astronomer Thomas Harriot (1560–1621) related to the binary number system. The various variants of the binary notation of numbers presented in the works, examples of converting a decimal number to a binary number and vice versa, examples of four arithmetic operations in the binary number system, the execution methods of which coincide with modern ones, as well as an example of multiplication by an original method, the name of which can be translated in Latin as "another method is sequential addition" are given. All this allows us to conclude that Thomas Harriot described the binary number system earlier than the great German scientist Gottfried Wilhelm Leibniz, who did so in his work "Explication de l'Arithmetique Binaire" in 1703.

Convergent series of integers with missing digits.

Abstract: A classical theorem of Kempner states that the sum of the reciprocals of positive integers with missing decimal digits converges. This result is extended to much larger families of "missing digits" sets of positive integers with convergent harmonic series.

Students Characters’ Development through Mathematics on the subjects of Decimal and Block

Abstract: The purpose of this research is to find the development of students’ characters’ through the uses of mathematics on the subjects of decimals and blocks in MIN Tungkop, Aceh Besar, specifically on the class V2. The subjects of this research are 9 students chosen out of 36, consist of 3 male students and 6 female students. The research data is collected through observation and interviews with the students. The data is analyzed using qualitative method based on the indicators of the observed characteristics. According to research, it is known that students characters’ did developed on the characters of democratic, independent, curiosity, creative thinking and critical thinking.

High Precision Binary Coded Decimal (BCD) unit for 128-bit addition

Abstract: Financial and business applications utilize decimal information and invest the majority of their energy in decimal number-crunching. Programming usage of decimal number-crunching is common, at any rate, multiple times slower than paired math actualized in equipment. This paper proposes a reduced delay binary coded decimal (BCD) adder that improves BCD addition delay by expanding parallel processing. The ordinary BCD adders are delayed because of the utilization of two binary adders. we structured and executed a new double mode BCD adder which utilizes just a single adder that produced the sum and sum+6. Using a pipeline procedure, an additional 128-bit BCD adder was implemented. The proposed BCD adder was planned and implemented using VHDL with XILINX 9.2 modification. The sequences of the regular BCD adder contrast with the proposed BCD adder. Experimental results show that the proposed BCD adder is 16.7% quicker than a traditional BCD adder. The proposed BCD 128-bit adder is 61.2% faster than the regular BCD 128 adder.

Criteria for the numerical constant recognition.

Abstract: The need for recognition/approximation of functions in terms of elementary functions/operations emerges in many areas of experimental mathematics, numerical analysis, computer algebra systems, model building, machine learning, approximation and data compression. One of the most underestimated methods is the symbolic regression. In the article, reductionist approach is applied, reducing full problem to constant functions, i.e, pure numbers (decimal, floating-point). However, existing solutions are plagued by lack of solid criteria distinguishing between random formula, matching approximately or literally decimal expansion and probable ''exact'' (the best) expression match in the sense of Occam's razor. In particular, convincing STOP criteria for search were never developed. In the article, such a criteria, working in statistical sense, are provided. Recognition process can be viewed as (1) enumeration of all formulas in order of increasing Kolmogorov complexity K (2) random process with appropriate statistical distribution (3) compression of a decimal string. All three approaches are remarkably consistent, and provide essentially the same limit for practical depth of search. Tested unique formulas count must not exceed 1/sigma, where sigma is relative numerical error of the target constant. Beyond that, further search is pointless, because, in the view of approach (1), number of equivalent expressions within error bounds grows exponentially; in view of (2), probability of random match approaches 1; in view of (3) compression ratio much smaller than 1.

IEEE 754-Based Single- and Double-Precision Floating-Point Multiplier Analysis

Abstract: In signal processing applications decimal and floating-point arithmetic units are of prominent importance. IEEE has developed the IEEE 754 standard for floating-point calculations. A revised standard IEEE 754r comes in 2008 for floating-point arithmetic units. Different conditions incorporated into the IEEE 754r have originated the novel IEEE 754-2008 standard (Eisen et al. in IBM J Res Dev 51(6):1–21, 2007) [1]. A vital operation in calculations of DFP is the multiplication due to its wide range of uses therefore in current years several decimal multiplication designs in fixed and floating-point have been proposed with different results maintaining a compromise between parameters such as latency and area. Hence studying and proposing innovative multiplication alternatives in DFP format is attractive to find suitable design compromises. This paper presents a general approach to floating-point decimal numbers that are represented in the IEEE 754-2008 standard. For FPGA implementation the Verilog code is developed and synthesized in Xilinx Virtex 4 and 7 series for DFP multiplier.

Method for determining temperature of beginning of change in indicators of thermal oxidative stability and maximum operating temperature of lubricants

Abstract: FIELD: technological processes.SUBSTANCE: invention relates to technology of determining indicators of thermal oxidative stability of lubricants. Disclosed is a method in which lubricant samples are thermostated at a minimum of three selected temperatures in the presence of air with mixing of constant weight for a period of time, at regular intervals the sample of the oxidised lubricant is weighed, part of sample is photometered and optical density, evaporation and coefficient of thermo-oxidative stability are determined. According to said indicators of thermal oxidative stability, calculating the amount of heat energy absorbed by oxidation products, evaporation products, and total absorbed heat energy during temperature control of lubricant, which is determined by product of temperature value, multiplied by test time and value of corresponding thermo-oxidative stability index. Decimal logarithms of absorbed heat energy are calculated for each index and graphical dependencies of decimal logarithm of absorbed heat energy of thermo-oxidative stability index on decimal logarithm of time and test temperature are plotted. These relationships are used to determine values of decimal logarithm of absorbed thermal energy of thermo-oxidative stability index at given decimal logarithm of test time and test temperatures. Values of the decimal logarithm of the test time are also determined at a given value of the decimal logarithm of the absorbed heat energy of the thermo-oxidative stability at each temperature. Besides, values of decimal logarithm of time of beginning of change of decimal logarithm of absorbed thermal energy of thermo-oxidative stability at each temperature are determined. Based on the obtained data, additional graphic relationships are plotted for each index. Dependence of the decimal logarithm of the absorbed heat energy of the thermo-oxidative stability value on the test temperature is used to determine the temperature of the beginning of the change in the decimal logarithm of the absorbed heat energy at a given decimal logarithm of the test time. Dependence of decimal logarithm of test time on test temperature with given value of decimal logarithm of absorbed thermal energy of thermo-oxidative stability is used to determine maximum operating temperature of analyzed lubricant, and based on the decimal logarithm of the beginning of the change in the decimal logarithm of the absorbed heat energy of the thermo-oxidative stability index from the test temperature, the beginning of the change in the decimal logarithm of the absorbed heat energy is predicted for other temperatures.EFFECT: high information content of lubricant control for comparison of their quality and selection.1 cl, 3 dwg, 1 tbl

Une situation qui problématise les passages discret-dense-continu

Abstract: This article presents an analysis of the discussion and written work produced during an experiment in which two students in teacher training were asked to solve a version of the fixed-point problem initially proposed by Pontille, Feurly-Reynaud and Tisseron. Our interest lies in how the problem can be broken down into five tasks (proposed by us), and specifically the effect of an intermediary phase involving the set of numbers that have a maximum of five decimal places. We are also interested in how the students reorient their mathematical work based on the hints and clues provided by the researchers. In our analysis, we discuss─as much from an epistemological perspective as from a cognitive perspective─the problem of how to conceptualize/coordinate the properties of density and completeness when it comes to extending the set of rational numbers to the set of real numbers. We are particularly interested in the property of density (intrinsic, with respect to order) in ordered sets D and Q and the role it can play in the learner's ability to separate the numerical-arithmetic structure of the theoretical “real axis” from its representation in the figural register, which, according to our analysis, is one of the key aspects in the conceptualization of R.

A Computational Criterion for the Irrationality of Some Real Numbers

Abstract: In this paper, we compute the asymptotic average of the decimals of some real numbers. With the help of this computation, we prove that if a real number cannot be represented as a finite decimal and the asymptotic average of its decimals is zero, then it is irrational. We also show that the asymptotic average of the decimals of simply normal numbers is 9/2.

Reversible data hiding scheme based on the AMBTC compression technique and Huffman coding

Abstract: This paper proposes a reversible data hiding (RDH) method based on the absolute moment block truncation coding (AMBTC) compression technique and Huffman coding. First, AMBTC is used to compress the original greyscale image to obtain two quantisation levels and a bitmap of each block. Next, the bitmap of each block is converted into a decimal number to calculate the frequency of the decimal number. A user-defined threshold is used to classify the block as embeddable or not. If the frequency of the decimal number is larger than or equal to the threshold, the bitmap is embeddable and is then compressed by the Huffman coding technology. The scheme takes the redundancy of each block by using the Huffman code instead of the bitmap to embed secret information. Experimental results show that our proposed scheme has a better hiding payload than other methods, as well as an acceptable image visual quality.

Local Comparative Decimal Pattern for Face Recognition

Abstract: Rapid growth of social networks has provided an extraordinary medium to share a large volume of photographs online. This calls for designing efficient face recognition techniques that are applicabl...