Search

This document exposes syntax of decimal error bug forms deep within AI's computer mainframe, which runs on none other than the dreaded Microsoft. Please switch to Macintosh or Linux immediately, as Unix is not susceptible to these kinds of error forms.

Using chaotic system for image encryption is a feasible and popular research interest. In this paper, a compound Sine-Piecewise Linear Chaotic Map is proposed to improve the chaotic characteristics of the original chaotic map. Compared with the original chaotic system, the proposed compound chaotic system has better dynamics performances, larger parameter space, which is more suitable for cryptographic applications. Furthermore, an image encryption algorithm based on this chaotic model and varying DNA coding is proposed. In this encryption algorithm, a novel method is provided to convert decimal numbers to binary numbers. Several numerical experiments show that the proposed encryption algorithm has good security performances, and is competitive with other chaos-based image encryption algorithms.

O presente artigo tem como objetivo apresentar resultados encontrados, ao longo de uma pesquisa de mestrado, a respeito dos conhecimentos mobilizados acerca do valor posicional no Sistema de Numeração Decimal (SND), por alunos de nove anos de idade. Como pressupostos teóricos, utilizamos as contribuições das pesquisas de Lerner e Sadovsky; Zunino e Brandt, que abordam a construção do valor posicional no SND por alunos dos anos iniciais do Ensino Fundamental. Baseados em uma metodologia qualitativa, aplicamos um instrumento composto por seis atividades. Os participantes mobilizaram conhecimentos relacionados à sequência numérica, aos critérios de comparação de Lerner e Sadovsky, ao valor posicional e à influência da numeração falada no registro escrito dos números. De acordo com as análises realizadas, podemos inferir que a construção do conhecimento sobre o valor posicional no SND é um processo longo e progressivo, não se resumindo a memorizar a sequência numérica.

The conversion of binary data to its equivalent decimal counterpart and the vice-versa is very essential and necessary for all optical/electrical computing and data processing systems. In this paper, the authors propose a new scheme for the optical conversion of frequency encoded binary data to its equivalent frequency encoded decimal form based on the optical tree architecture. This is completely associated with frequency encoding technique because of its salient advantages. The scheme is implemented with all optical nonlinear switch like Mach–Zehnder interferometer-based semiconductor optical amplifier (MZI-SOA) to get a faster conversion rate.

Air Canada managed to have a passenger aircraft run out of fuel in mid-air due to confusion about metric units (Stephenson in Mars climate orbiter mishap investigation board phase I report, NASA, 1999), and NASA lost an entire spacecraft due to a misunderstanding amongst engineers about the units used in the propulsion system design (Witkin in Jet’s fuel ran out after metric conversion errors, The New York Times, 1983). Measurements only make sense if the units are correct and well-defined. A unit of measurement is a definite magnitude of a quantity, defined by convention or law. Any other quantity of that kind can then be expressed as a multiple or submultiple of the unit of measurement. The Egyptians used the Farao as definite magnitude, while many years later, the french revolutionists introduced the earth as a reference and laid the foundations for the modern decimal system. Since recently, we have a truly universal and stable system that uses physics’s natural constants and laws to define the base units of measurement. This paper explains how this new concept works and how it is implemented in practice.

Działalność bibliograficzna ks. Idziego Radziszewskiego stanowiła ważny etap w jego naukowej biografii. W latach 1905–1906 opublikował on na łamach „Przeglądu Filozoficznego” „Polską Bibliografię Filozoficzną” w układzie według klasyfikacji dziesiętnej. Podejmując tego typu pracę, chciał Radziszewski wydobyć z zapomnienia polski dorobek w dziedzinie filozofii i przybliżyć go światu naukowemu za granicą. Pierwowzorem dla jego przedsięwzięcia stała się międzynarodowa bieżąca bibliografia filozoficzna wydawana przez Wyższy Instytutu Filozoficzny w Lowanium, z którą miał okazję zapoznać się podczas swojego pobytu w Belgii. W historii filozofii i bibliografii polskiej praca I. Radziszewskiego stanowi pierwszą próbę bieżącej rejestracji polskiej produkcji filozoficznej. Po raz pierwszy też na gruncie polskim przy sporządzaniu spisu bibliograficznego zastosowana została klasyfikacja dziesiętna.

The research was aimed to investigate six-lesson study team members in designing mathematical activities to develop students’ mathematization using Open Approach in the second step of the Lesson Study process in teaching decimal numbers. A total of 16 Grade 4 students participated as the target group. Three instruments were used namely lesson plans, student worksheets, and observation field notes. Researchers employed ethnographic research design to study how the mathematical activities could assist students to develop their mathematical ideas from the real world to the mathematical world through a flow of lessons over the four stages of the Open Approach along with the Lesson Study process. The research results revealed that a series of five research lesson plans encompassing various mathematical activities were successfully encouraging students to elaborate their ideas and transmitting their ideas from the real-world to the mathematical world using semi-concrete aids. Moreover, the results of using the Open Approach have been proved to be relevant as students demonstrated their mathematization in fostering their mathematical thinking to transform their ideas smoothly. Therefore, designing mathematical activities is important to cultivate students’ mathematical thinking in problem-solving instantaneously. A limitation of the research was identified when the Lesson Study team members were reflecting on the teaching practice. This is because they found that the unclear illustration in the student worksheets has raised confusion. In conclusion, the overall results of this research have contributed significantly to our recognition of the practicality of Open Approach treatment in the Lesson Study process in developing students’ mathematization through their participation in mathematical activities.

Novel partial product generation scheme has been proposed for decimal multiplication where positional digit conversion methodology has been utilized. Moreover, through the proposed methodology 16 × 16 decimal digit multiplier has been introduced, where unconventional (4221) binary-coded decimal (BCD) number system has been focused. To implement the multiplication technique, multiplication digits have been converted into two decimal digits based on the corresponding bit weights. In addition with that, in partial product addition stage, optimized decimal digit compressors have been utilized. Besides that, mathematical expressions have been introduced for decimal ripple carry adder and through that final addition has been carried out. The proposed techniques also summarize the performances parameter matrices in terms of propagation delay, power, area and power delay product. Comparative analysis from its counterpart also has been addressed.

The paper investigates a nonlinear substitution transformation, presented as an element of the number system of factorial sets. This approach takes into account the characteristic features of substitutions and al-lows you to minimize the amount of memory for storing. Based on the unambiguous numbering approach for substitutions, three methods of storing in memory are considered: in the form of a vector, in the form of values of cyclic shifts of elements of an identical substitution, and in the form of a decimal substitution number. The results of the analysis of the amount of data required for storing the nonlinear substitution transformation for cryptographic primitives are presented. The complexity of translating the transformed substitutions into the standard form of storage by a vector is determined. The obtained results can be ap-plied in software solutions for ensuring information security using cryptographic primitives containing a nonlinear substitution transformation. The proposed approach to writing in the form of substitution trans-formations is recommended for implementation in complexes with a limited amount of memory.

Using the design method proposed by Kunii, this study mathematically explains the achievement of Kublai of merging two different societies to build a globalized nation after conquering China. The considered design method, called incrementally modular abstraction hierarchy, consists of seven levels, from the most abstract, homotopy, to the most concrete, computer graphics. Moreover, it allows a flexible design while moving up and down its hierarchy. Using this method, we attempt to restore the concepts of Kublai, aiming to build a globalized state by combining nomadic and agricultural cultures. Specifically, we examine the use of two capitals to resolve the problem of different lifestyles of the Mongolian Khan, who moved between the summer and winter camps of the nomads, and the Chinese Emperor, who lived in a fixed palace of the agricultural people. By incorporating the category theory into Kunii’s method, we discuss the adjunction of the Mongolian 1000-household social and military system based on decimal numbers with the Chinese bureaucratic system. The inclusion of the category theory in his original method allows visualization by programming, making the design more versatile and flexible.

The historical problem of Tamil literature is still unresolved among many literary critics and is full of differences of opinion. Among them, the period of Sangam literature and the news of the Apuls are the most controversial. Various reports have been circulating by critics about Kapil, who has sung a number of Sangam songs and is notable for his fame. There are a number of issues with Kapilar's Kurinchipattu reference to it. The purpose of this article is to explore typography. It is noticeable that decimal texts are referred to Kurinchipattu as reference ciphers when they are segmented on a material basis. This is also the case with the description of the Pattuppaṭṭu when they are known in the order of the singers and the singers. The tagline is Kurinchipattu in the field of ‘Thozhi Arathodu Nittral’

SimRank is a popular measurement for evaluating the node-to-node similarities based on the graph topology. In recent years, single-source and top-k SimRank queries have received increasing attention due to their applications in web mining, social network analysis, and spam detection. However, a fundamental obstacle in studying SimRank has been the lack of ground truths. The only exact algorithm, Power Method, is computationally infeasible on graphs with more than $$10^6$$ nodes. Consequently, no existing work has evaluated the actual accuracy of various single-source and top-k SimRank algorithms on large real-world graphs. In this paper, we present ExactSim, the first algorithm that computes the exact single-source and top-k SimRank results on large graphs. This algorithm produces ground truths with precision up to 7 decimal places with high probability. With the ground truths computed by ExactSim, we present the first experimental study of the accuracy/cost trade-offs of existing approximate SimRank algorithms on large real-world graphs and synthetic graphs. Finally, we use the ground truths to exploit various properties of SimRank distributions on large graphs.

This paper reports a method to solve ordinary fourth-order differential equations in the form of ordinary power series and, for the case of regular special points, in the form of generalized power series. An algorithm has been constructed and a program has been developed in the MAPLE environment (Waterloo, Ontario, Canada) in order to solve the fourth-order differential equations. All types of solutions depending on the roots of the governing equation have been considered. The examples of solutions to the fourth-order differential equations are given; they have been compared with the results available in the literature that demonstrate excellent agreement with the calculations reported here, which confirms the effectiveness of the developed programs. A special feature of this work is that the accuracy of the results is controlled by the number of terms in the power series and the number of symbols (up to20) in decimal mantissa in numerical calculations. Therefore, almost any accuracy allowed for a given electronic computing machine or computer is achievable. The proposed symbolic-numerical method and the work program could be successfully used for solving eigenvalue problems, in which controlled accuracy is very important as the eigenfunctions are extremely (exponentially) sensitive to the accuracy of eigenvalues found. The developed algorithm could be implemented in other known computer algebra packages such as REDUCE (Santa Monica, CA), MATHEMATICA (USA), MAXIMA (USA), and others. The program for solving ordinary fourth-order differential equations could be used to construct Green’s functions of boundary problems, to solve differential equations with private derivatives, a system of Hamilton’s differential equations, and other problems related to mathematical physics.

Fraction and decimal number learning are notoriously difficult for elementary-aged students. Fraction Ball represents a new way to engage children in fraction and decimal number learning that is playful, engaging, embodied, physically active, and rooted in cognitive science research. In our work, we provide evidence for the efficacy of Fraction Ball in promoting rational number learning through a rigorous experimental design. We also demonstrate ways in which the schoolyard is conducive to play-based interventions that can supplement classroom instruction to truly integrate learning across academic domains using an engaging and evidence-based approach. Importantly, this study serves as a model for how interventionists can engage educators as partners in intervention design and iterative implementation to improve learning outcomes for students and create useful educational innovations for teachers. Fraction Ball is affordable, easy to disseminate, and has the potential to promote rational number learning on a global scale.

Understanding fraction magnitudes is important for achievement and in daily life. However, adults' fraction reasoning sometimes appears to reflect whole number bias and other times reflects accurate reasoning. In the current experiments, we examined how contextual factors and individual differences in executive functioning (Experiment 1), knowledge of fraction equivalence (both experiments), and strategy use (Experiment 2) influenced adults' fraction reasoning. Adults were only biased by fraction components when reasoning about fractions as holistic magnitudes was difficult: when estimating under a time constraint, when estimating fractions with large components, or when comparing fractions close in decimal distance. However, adults' knowledge of fraction equivalence moderated the effects of whole number components on their fraction estimation performance: when modeled at low levels of equivalence knowledge, adults were biased by fraction components when estimating. Adults with more knowledge of fraction equivalence were able to reason about fractions as holistic magnitudes through adaptive strategy choices. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

International audience; Le tableau de numération semble être un support pédagogique usuel à l’école primaire, à tous les niveaux d’enseignement. La recherche en fait rarement un objet d’étude à part entière. Nous interrogeons dans ce texte la place et le rôle qu’a et que pourrait avoir le tableau de numération pour l’apprentissage de la compréhension de l’écriture chiffrée à l’école primaire. Pour cela nous avons enquêté sur les usages du tableau dans l’enseignement à partir de quelques manuels et en recueillant des éléments de pratiques déclarées à partir d’un questionnaire proposé à des enseignants. Ce travail a été complété par une recherche de traces de tableau de numération dans l’histoire des nombres et de ses usages, en nous appuyant sur quelques travaux d’historiens et d’épistémologues. Ceci nous amène à dégager des potentialités didactiques du tableau de numération, et à proposer des pistes pour en renouveler les formes et les usages.

Background: Specific language impairment (SLI) diagnosis is inconvenient due to manual procedures and hardware cost. Computer-aided SLI diagnosis has been proposed to counter these inconveniences. This study focuses on evaluating the feasibility of computer systems used to diagnose SLI. Methods: The accuracy of Webgazer.js for software-based gaze tracking is tested under different lighting conditions. Predefined time delays of a prototype diagnosis task automation script are contrasted against with manual delays based on human time estimation to understand how automation influences diagnosis accuracy. SLI diagnosis binary classifier was built and tested based on randomised parameters. The obtained results were cross-compared to Singlims_ES.exe for equality. Results: Webgazer.js achieved an average accuracy of 88.755% under global lighting conditions, 61.379% under low lighting conditions and 52.7% under face-focused lighting conditions. The diagnosis task automation script found to execute with actual time delays with a deviation percentage no more than 0.04%, while manually executing time delays based on human time estimation resulted in a deviation percentage of not more than 3.37%. One-tailed test probability value produced by both the newly built classifier and Singlims_ES were observed to be similar up to three decimal places. Conclusion: The results obtained should serve as a foundation for further evaluation of computer tools to help speech language pathologists diagnose SLI.

Digital learning games are designed to foster both student learning and enjoyment. Given this goal, an interesting research topic is whether game mechanics that promote learning and those that promote enjoyment have different effects on students’ experience and learning performance. We explored these questions in Decimal Point, a digital learning game that teaches decimal numbers and operations to 5th and 6th graders, through a classroom study with 159 students and two versions of the game. One version encouraged playing and learning through an open learner model (OLM, N = 55), while one encouraged playing for enjoyment through an analogous open enjoyment model (OEM, N = 54). We compared these versions to a control version that is neutral with respect to learning and enjoyment (N = 50). While students learned in all three conditions, our results indicated no significant condition differences in learning outcomes, enjoyment, or engagement. However, the learning-oriented group engaged more in re-practicing, while the enjoyment-oriented group demonstrated more exploration of different mini-games. Further analyses of students’ interactions with the open learner and enjoyment models revealed that students who followed the learner model demonstrated better in-game learning and test performance, while following the enjoyment model did not impact learning outcomes. These findings indicate that emphasizing learning or enjoyment can lead to distinctive game play behaviors, and that open learner models can be helpful in a learning game context. In turn, our analyses have led to preliminary ideas about how to use AI to provide recommendations that are more aligned with students’ dynamic learning and enjoyment states and preferences.

Decimal converter plays an essential role in decimal arithmetic operations. A decimal converter is used to convert binary partial products to Binary Coded Decimal. Here, the use of the converter ce...

Freezing and crystallization of commercial ethylene carbonate-based binary electrolytes, leading to irreversible damage to lithium-ion batteries (LIBs), remain a significant challenge for the survi...

This study investigated relations between the distribution of practice problems in textbooks and students’ learning of decimal arithmetic. In Study 1, we analyzed the distributions of decimal arithmetic practice problems that appeared in 3 leading math textbook series in the United States. Similar imbalances in the relative frequencies of decimal arithmetic problems were present across the 3 series: Addition and subtraction more often involved 2 decimals than a whole number and a decimal, but the opposite was true for multiplication and division. We expected children’s learning of decimal arithmetic to reflect these distributional biases. In Studies 2, 3, and 4, we tested the prediction that children would have more difficulty solving types of problems that appeared less frequently in textbooks, regardless of the intrinsic complexity of solving the problems. We analyzed students’ performance on decimal arithmetic from an experiment conducted in a different lab 35 years ago (Study 2), from a contemporary large-scale web-based learning platform (Study 3), and from a recent controlled experiment conducted in our own lab (Study 4). Despite many differences among the 3 studies, performance in all 3 was in accord with the predictions. These findings suggest that the distributions of practice problems in math textbooks may influence what children do and do not learn. Usefulness of analyzing textbook problem distributions as well as educational implications of the current findings are discussed. (PsycInfo Database Record (c) 2021 APA, all rights reserved)

The article describes in detail the methods of extracting square and cube roots in the binary number system. The method for extracting the square root of a binary number is similar to the corresponding method for decimal numbers, which is called the "column method". As for decimal numbers, when choosing the next digit of the root, twice the current value of the root, represented in the binary system, is used. When extracting the cube root (also "column"), there are two differences from the decimal system. The first is that instead of 300 (the product of 3 and 100), the binary number 1100 is used (that is, the product of the binary equivalents of the numbers 3 and 4). The second difference is that instead of the number 30 (the product of 3 and 10), the binary number 110 is used (that is, the product of binary analogs numbers 3 and 2). To facilitate the selection of the next root digit (0 or 1), a number of standard values have been calculated, depending on the current root value. Assignments for independent work of students are offered.

We propose the approximation of $$\tanh$$ (i.e. the hyperbolic tangent) by specific formation of cubic splines. Thus, we save many multiplications and a division required for the standard double precision evaluation of this function. The cost we have to pay is to admit at most 2–4 decimal digits of accuracy in the final approximation. As a result, a speeding in neural networks performance is experienced after implementing this new approximant as transfer function.

This paper presents theoretical backgrounds of the symmetric encryption based on the residue number system. The peculiarities of this approach are that in the case of restoring a decimal number based on its residuals using the Chinese remainder theorem, multiplication occurs by arbitrarily chosen coefficients (keys). It is established that cryptostability of the developed methods is determined by the number of modules and their bit size. In addition, the described methods are found to allow to almost indefinitely increase the block of plain text for encryption, which eliminates the necessity to use different encryption modes.

The purpose of this study was to describe the students error on inversely proportional question at grade VIII F SMP Negeri 9 Palu. This type of research is qualitative research. Data were collected using data collection techniques, namely tests and interviews. The research subjects consisted of 3 people, namely C students, HD students and YYA students. The results of the study based on the students completion showed the mistakes made by the students in solving the comparison questions against the scores that were done. Based on the solution, conceptual and procedural errors were obtained. Conceptual errors include: a) factual errors consisting of: 1) students have not been able to write down the information contained in the questions, 2) students have not been able to understand the use of the equal sign correctly, 3) students have not been able to change the information contained in the questions into a model mathematics and 4) students have not been able to write conclusions correctly. b) Misconceptions consist of: 1) students do not understand the concept of reversing value comparisons, namely students working on comparison questions of turning values ​​using the principle of value comparisons, 2) students have not been able to operate a reversed value comparison and 3) students do not understand the concept of multiplication and division of integers and decimal numbers. Procedural errors consist of: 1) students have not been able to work on questions using the principle of reversing value comparisons, 2) students make mistakes operating multiplication and division and 3) students have not been able to determine the final result correctly.

Decimal multiplication is the most common operation in arithmetic applications. This paper presents an area-efficient digit-by-digit decimal multiplier using a modified binary-coded decimal digit multiplier. In general, a Binary-Coded Decimal (BCD) digit multiplier consists of two kinds of block, namely binary multiplier, and Partial Product Binary-to-Decimal (PPBD) converter. In the BCD digit multiplier design, the binary multiplier produces the partial product output by multiplying the multiplier value along with multiplicand, and the PPBD converter used to convert the binary partial product into the decimal value. Instead of the binary multiplier, this paper proposes a constant multiplier design to generate binary partial product values. Here, the multiplier value considers as the constant value. Further, the proposed architectures design and implement using both Field-Programmable Gate Array (FPGA) and Application Specific Integrated Circuit (ASIC). When compared with the existing methods, the implementation results show that the proposed design effectively reduces the area requirement and delay.

Decimal multiplication is one of the complex operations in the applications that still radix-10 representations are preferred. To improve the performance, Ahmed et al. proposed some fast and area efficient binary-to-decimal converters to be used for both partial product generation and partial product reduction stages of digit-by-digit decimal multiplication. These converters that transform each binary result to binary coded decimal (BCD) representation utilize two new types of binary-to-decimal converter cells in a cascading structure. These cells are called fast binary-to-decimal (FBD) and low-area binary-to-decimal (LABD) converters. In this paper, we show that despite the fact that their architectural framework for digit-by-digit decimal multiplication and the proposed hybrid multi-operand binary-to-decimal converter are correct, some logical equations presented for FBD converter cell are incorrect. Moreover, there exist ambiguities in presenting the logical equations of both FBD and LABD converter cells. Thus, we represent the correct and optimized equations for FBD and LABD converter cells using truth tables.

Exponential integral for real arguments is evaluated by employing a fast-converging power series originally developed for the resolution of Grandi’s paradox. Laguerre’s historic solution is first recapitulated and then the new solution method is described in detail. Numerical results obtained from the present series solution are compared with the tabulated values correct to nine decimal places. Finally, comments are made for the further use of the present approach for integrals involving definite functions in denominator.

Image representation is an active research area in the field of image processing. This paper proposes a novel image representation method under a non-standard positional numeral system, wherein complex numbers are used as bases in such non-standard positional numeral system. It is different with binary code and decimal code, where the digit 2 is used as the base in the binary system, and the digit 10 is used as the base in the decimal system. In the proposed image representation method, a two-dimensional image is transformed into a one-dimensional 0 $\sim$ 1 sequence, and its Gaussian integer is calculated based on the derived one-dimensional 0 $\sim$ 1 sequence. On the contrary, the original two-dimensional image can be recovered from its Gaussian integer. When images are represented as Gaussian integers, the classical geometrical operations are introduced into image processing. Then, the relationship of different images is established by the methods of plane geometry, i.e., the addition, subtraction, multiplication, division, conjugate, and inverse operations of images are defined. The experimental results show that the selection of complex number as base in the positional numeral system is a very special coding method, a given digital image is effectively converted to a Gaussian integer by using the proposed image representation method, and the image arithmetic is also successfully achieved. In addition, three applications based on the proposed image representation method including image camouflage, image sharing, and image scrambling are selected to demonstrate that the new image representation has good and potential practical applicability in the field of secure encryption of digital images.