Showing papers on "Decimal published in 2021"

A novel statistical decimal pattern-based surface electromyogram signal classification method using tunable q-factor wavelet transform

Abstract: Surface electromyogram sensors have been widely used to acquire hand gestures signals. Many machine learning and artificial intelligence methods have been presented for automated surface electromyogram signals classification. In this method, a novel surface electromyogram signals recognition method is presented using a novel 1D local descriptor. The proposed descriptor is called as statistical decimal pattern and it is utilized as feature extractor in this study and tunable q-factor wavelet transform is used as pooling in this method. By using tunable q-factor wavelet transform and the proposed statistical decimal pattern, a multileveled learning method is constructed. Ten levels are created by using tunable q-factor wavelet transform. Statistical decimal pattern extracts features from tunable q-factor wavelet transform sub-bands of the raw surface electromyogram signal. Then, the generated features are concatenated, and to select distinctive features, ReliefF and neighborhood component analysis are used together. In the classification phase, k-nearest neighbor classifier with city block distance is chosen. To test performance of the proposed tunable q-factor wavelet transform and the proposed statistical decimal pattern-based surface electromyogram classification method, a freely and publicly published dataset was used. In this dataset, 10 hand gestures were defined. Experimental results clearly shown that the proposed tunable q wavelet transform and statistical decimal pattern-based method achieved 98.0%, 99.79% accuracy rates on two datasets and it outcomes other state-of-the-art methods according to these results.

Distributions of textbook problems predict student learning: Data from decimal arithmetic.

Abstract: 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)

Efficiently inaccurate approximation of hyperbolic tangent used as transfer function in artificial neural networks

Abstract: 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.

An alternative approach for binary to decimal conversion of frequency encoded optical data using MZI-SOA Switch

Abstract: 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.

Symmetric Cryptoalgorithms in the Residue Number System

Abstract: 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.

Design and implementation of modified BCD digit multiplier for digit-by-digit decimal multiplier

Abstract: 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.

Origin of Irrational Numbers and Their Approximations

Abstract: In this article a sincere effort has been made to address the origin of the incommensurability/irrationality of numbers. It is folklore that the starting point was several unsuccessful geometric attempts to compute the exact values of 2 and π. Ancient records substantiate that more than 5000 years back Vedic Ascetics were successful in approximating these numbers in terms of rational numbers and used these approximations for ritual sacrifices, they also indicated clearly that these numbers are incommensurable. Since then research continues for the known as well as unknown/expected irrational numbers, and their computation to trillions of decimal places. For the advancement of this broad mathematical field we shall chronologically show that each continent of the world has contributed. We genuinely hope students and teachers of mathematics will also be benefited with this article.

Number Parsing at a Gigabyte per Second

Abstract: With disks and networks providing gigabytes per second, parsing decimal numbers from strings becomes a bottleneck. We consider the problem of parsing decimal numbers to the nearest binary floating-point value. The general problem requires variable-precision arithmetic. However, we need at most 17 digits to represent 64-bit standard floating-point numbers (IEEE 754). Thus we can represent the decimal significand with a single 64-bit word. By combining the significand and precomputed tables, we can compute the nearest floating-point number using as few as one or two 64-bit multiplications. Our implementation can be several times faster than conventional functions present in standard C libraries on modern 64-bit systems (Intel, AMD, ARM and POWER9). Our work is available as open source software used by major systems such as Apache Arrow and Yandex ClickHouse. The Go standard library has adopted a version of our approach.

A Novel Image Representation Method Under a Non-Standard Positional Numeral System

Abstract: 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.

Influence of a function's coefficients and feedback of the mathematical work when reading a graph in an online assessment system

Abstract: This paper shows the results of an experiment applied to 170 students from two Chilean universities who solve a task about reading a graph of an affine function in an online assessment environment where the parameters (coefficients of the graphed affine function) are randomly defined from an ad-hoc algorithm, with automatic correction and automatic feedback. We distinguish two versions: one of them with integer coefficients and the other one with decimal coefficients in the affine function. We observed that the nature of the coefficients impacts the mathematical work used by the students, where we again focus on two of them: by direct estimation from the graph or by calculating the equation of the line. On the other hand, a feedback oriented towards the "estimation" strategy influences the mathematical work used by the students, even though a non-negligible group persists in the "calculating" strategy, which is partly explained by the perception of each of the strategies.

Number Parsing at a Gigabyte per Second

Abstract: With disks and networks providing gigabytes per second, parsing decimal numbers from strings becomes a bottleneck. We consider the problem of parsing decimal numbers to the nearest binary floating-point value. The general problem requires variable-precision arithmetic. However, we need at most 17 digits to represent 64-bit standard floating-point numbers (IEEE 754). Thus we can represent the decimal significand with a single 64-bit word. By combining the significand and precomputed tables, we can compute the nearest floating-point number using as few as one or two 64-bit multiplications. Our implementation can be several times faster than conventional functions present in standard C libraries on modern 64-bit systems (Intel, AMD, ARM and POWER9). Our work is available as open source software used by major systems such as Apache Arrow and Yandex ClickHouse. The Go standard library has adopted a version of our approach.

Profiles in understanding operations with rational numbers

Abstract: Students often show difficulties in understanding rational numbers Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational

The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in Brazil

Abstract: In this research we investigate how mathematics teachers, as graduate students, estimate the value of π by exploring the problem of squaring the circle using digital technology. Initially, we mention some aspects of teaching and learning of calculus in the literature, emphasizing studies that use the notion of humans-with-media to highlight the role of technology in mathematical thinking and knowledge production. Insights on the history of mathematics in calculus are also discussed. We developed a qualitative study based on three different solutions created by groups of teachers using the software GeoGebra and Microsoft Excel. All the teachers’ solutions improved the approximation (8/9)2 $$\approx$$ π/4, by determining p and q for (p/q)2 $$\approx$$ π/4. The first two solutions with GeoGebra emphasized experimentation and visualization, improving the approximation from one to three decimal places. The third solution with Excel pointed out the elaboration of a formula and improved it up to six decimal places. We emphasize how media shaped the strategies and solutions of the groups. Based on these solutions, we explore an approach for cubing the sphere, discussing approximations for π, highlighting the role of media in enhancing conceptual complexity in the solution of mathematical problems. The nature of the strategies for solving a problem is discussed, especially regarding different ways of thinking-with-technology developed by collectives of teachers-with-media. Although we acknowledge an alternative design for the proposed task, the exploration of problems using aspects of the history of mathematics contributes to the state of the art concerning the studies in calculus developed by the Research Group on Technology, other Media, and Mathematics Education in Brazil.

On the Buck-Stopping Identification of Numbers

Abstract: Kripke observes that the decimal numerals have the buck-stopping property: when a number is given in decimal notation, there is no further question of what number it is. What makes them special in this way? According to Kripke, it is because of structural revelation: each decimal numeral represents the structure of the corresponding number. Though insightful, I argue, this account has some counterintuitive consequences. Then I sketch an alternative account of the buck-stopping property in terms of how we specify the positions of numbers in the progression.

Hardware–Software Co-Design for Decimal Multiplication

Abstract: Decimal arithmetic using software is slow for very large-scale applications. On the other hand, when hardware is employed, extra area overhead is required. A balanced strategy can overcome both issues. Our proposed methods are compliant with the IEEE 754-2008 standard for decimal floating-point arithmetic and combinations of software and hardware. In our methods, software with some area-efficient decimal component (hardware) is used to design the multiplication process. Analysis in a RISC-V-based integrated co-design evaluation framework reveals that the proposed methods provide several Pareto points for decimal multiplication solutions. The total execution process is sped up by 1.43× to 2.37× compared with a full software solution. In addition, 7–97% less hardware is required compared with an area-efficient full hardware solution.

New Center Folding Strategy Encoding for Reversible Data Hiding in Dual Stego Images

Abstract: A new center folding encoding technique used for dual stego image is proposed. This proposed encoding technique aims to minimize distortion caused due to the changes made in the pixel while embedding. As the modification in pixel intensity reduces, the distortion of these stego images also reduces. This outline, first, combines the data bits and converts to decimal to obtain the decimal intensity. The index is generated from the decimal intensity using the intensity reduction process. The index is further converted to an encoded index, and it is hidden on the cover image. During the extraction stage, the encoded index is extracted after the dual stego images and it is renewed to index. The decimal intensity is reconstructed from the index using the intensity reconstruction process. Finally, the decimal intensity values are transformed to binary to estimate the secret image. The performance evaluation of the proposed dual stego reversible data hiding (RDH) was done using the factors such as peak signal-to-noise ratio (PSNR) and embedding rate.

Investigations on Decimal Multipliers through Novel Partial Product Generators

Abstract: 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.

Origin, Alternative Expressions of Newcomb-Benford Law and Deviations of Digit Frequencies

Abstract: The Newcomb-Benford law, which describes the uneven distribution of the frequencies of digits in data sets, is by its nature probabilistic. Therefore, the main goal of this work was to derive formulas for the permissible deviations of the above frequencies (confidence intervals). For this, a previously developed method was used, which represents an alternative to the traditional approach. The alternative formula expressing the Newcomb-Benford law is re-derived. As shown in general form, it is numerically equivalent to the original Benford formula. The obtained formulas for confidence intervals for Benford’s law are shown to be useful for checking arrays of numerical data. Consequences for numeral systems with different bases are analyzed. The alternative expression for the frequencies of digits at the second decimal place is deduced together with the corresponding deviation intervals. In general, in this approach, all the presented results are a consequence of the positionality property of digital systems such as decimal, binary, etc.

Design of synchronous decimal counter using reversible Toffoli–Fredkin Netlist

Abstract: Investigations in reversible computation have been one of the notable dimensions among the emerging research domains. Reversible circuits promise near-zero heat dissipation resulting in a considerable amount of literary proposals. This article proposes a reversible synchronous decimal counter using Toffoli and Fredkin gates. Decimal counter forms an important Boolean specification as they are used for clock generators, frequency dividers, clock division, integrated oscillation, etc. Although literature witnesses exhaustive research in reversible mod-2/4/8/16 counters, there is a void in the domain of reversible decimal counters. We propose three designs D1, D2, and D3. Design D1 and D2 are synchronous decimal up and down counters, respectively, using Toffoli Netlist. Design D3 is the integration of designs D1 and D2 using the Fredkin Gate array. The proposed designs have been checked using a state-of-the-art optimization algorithm in literature and the results reflect our design to be best optimized. Peer analysis reflects a summary of existing literary proposals exhibiting the uniqueness of the proposed designs.

Encryption of 3d plane in gis using voronoi-delaunay triangulations and catalan numbers

Abstract: A method of encryption of the 3D plane in Geographic Information Systems (GIS) is presented. The method is derived using Voronoi-Delaunay triangulation and properties of Catalan numbers. The Voronoi-Delaunay incremental algorithm is presented as one of the most commonly used triangulation techniques for random point selection. In accordance with the multiple applications of Catalan numbers in solving combinatorial problems and their "bit-balanced" characteristic, the process of encrypting and decrypting the coordinates of points using the Lattice Path method (walk on the integer lattice) or LIFO model is given. The triangulation of the plane started using decimal coordinates of a set of given planar points. Afterward, the resulting decimal values of the coordinates are converted to corresponding binary records and the encryption process starts by a random selection of the Catalan key according to the LIFO model. These binary coordinates are again converted into their original decimal values, which enables the process of encrypted triangulation. The original triangulation of the plane can be generated by restarting the triangulation algorithm. Due to its exceptional efficiency in terms of launching programs on various computer architectures and operating systems, Java programming language enables an efficient implementation of our method.

A New Efficient Numbering System : Application to Numbers Generation and Visual Markers Design.

Abstract: This short paper introduces a recently patented line based numbering system. The last allows a best concordance with decimal digits values, and open up new opportunities, which are not possible with the classical decimal numeration system. Proposed OILU symbolic allows generating a new type of number series, based on multi facets numbers splitting process. On the other hand, this new symbolic is used in the development of new visual markers, highly required in augmented reality and UAV's navigation applications.

On the efficient parallel computing of long term reliable trajectories for the Lorenz system.

Abstract: In this work we propose an efficient parallelization of multiple-precision Taylor series method with variable stepsize and fixed order. For given level of accuracy the optimal variable stepsize determines higher order of the method than in the case of optimal fixed stepsize. Although the used order of the method is greater then that in the case of fixed stepsize, and hence the computational work per step is greater, the reduced number of steps gives less overall work. Also the greater order of the method is beneficial in the sense that it increases the parallel efficiency. As a model problem we use the paradigmatic Lorenz system. With 256 CPU cores in Nestum cluster, Sofia, Bulgaria, we succeed to obtain a correct reference solution in the rather long time interval - [0,11000]. To get this solution we performed two large computations: one computation with 4566 decimal digits of precision and 5240-th order method, and second computation for verification - with 4778 decimal digits of precision and 5490-th order method.

A possible use of the cubit rod in Ancient Egypt to measure and draw lengths based on fractions

Abstract: We will discuss about a possible method of using the cubit rod by the architects and the surveyors of Ancient Egypt to measure and draw lengths, comparing it with the other interpretations present in Literature. Instead of the modern decimal notation, which sees the use of comma to represent a number or a measure, at that time there was a wide use of fractions in calculations. The current work proposes that, through the cubit rod and its partitions of the finger into fractions, it could be possible to obtain very accurate measurements.

Evaluation of Exponential Integral by Means of Fast-Converging Power Series

Abstract: 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.

Multi - objective distribution network reconstruction based on decimal coding

Abstract: The distribution network reconfiguration problem is a highly complex mixed integer, nonlinear, multi-objective planning problem. According to the closed-loop design and open-loop operation of the distribution network, this paper proposes a loop- based decimal coding method to reduce the space of infeasible solutions. At the same time, combined with breadth-first search to form and test feasible solutions. The text takes the network loss and voltage deviation as the target, uses the NSGA-II algorithm for multi-objective optimization, and uses the Newton Raphson method to check and evaluate the reconstruction scheme. Finally, an IEEE-33 node test case is used to verify the algorithm. The results show that the algorithm can quickly calculate an approximate global optimal network reconstruction scheme.

Method to determine flash point of lubricating oils

Abstract: FIELD: test technology.SUBSTANCE: invention relates to the field of materials testing by means of heating, in particular to the technology of determining the flash point temperature of lubricating oils without use of firing of vapors, and can be used in evaluation of operational characteristics of commercial and operating lubricants. Disclosed is a method for determining flash point of lubricating oils, in which samples of lubricating oil of constant weight are thermostatically controlled at atmospheric pressure without mixing for a period of time, providing evaporation of the installed mass of lubricating oil. After equal time intervals of the test, the temperature-controlled sample is weighed, the weight of evaporated lubricating oil is determined, graphical dependencies of the weight of evaporated lubricating oil on time and temperature of temperature control are plotted. Obtained dependences are used to determine decimal logarithms of thermal energy absorbed by the mass of evaporated oil determined by the product of temperature for the set time and weight of the evaporated oil during that time. Graphical dependences of the decimal logarithm of heat energy absorbed by the evaporated oil mass are plotted against the decimal logarithm of the set time and temperature of temperature control. Values of decimal logarithms of thermal energy are determined at crossing of these dependencies with axis of ordinates. Constructing the graphical dependence of these values on the temperature control temperature, from which the temperature of the beginning of the change in the decimal logarithm of heat energy is determined. Also, at least three constant values of decimal logarithm of heat energy for analyzed oil are determined, from which values of decimal logarithms of time for achievement of selected constant values of decimal logarithm of heat energy for investigated temperatures of temperature control are determined. Graphical dependences of the decimal logarithm of time for achieving selected constant values of the decimal logarithm of heat energy absorbed by the mass of evaporated lubricating oil are plotted against temperature of thermal conditioning, and from points of intersection of given relationships with the axis of abscissa determining flash points and their dependence on the accepted constant values of the decimal logarithm of heat energy, based on which graphical dependence of constant values of decimal logarithm of heat energy absorbed by mass of evaporated oil is plotted, from the flash temperature, from which the effect of the decimal logarithm of heat energy on the flash point is determined, which enables to justify the choice of the value of the decimal logarithm of heat energy for comparison of different lubricating oils.EFFECT: high accuracy of the method of determining flash point of lubricating oils by taking into account heat energy absorbed by the mass of evaporated oil and information on the temperature of the onset of evaporation processes.1 cl, 15 dwg

A number system with base $-\frac32$.

Abstract: In the present paper we explore a way to represent numbers with respect to the base $-\frac32$ using the set of digits $\{0,1,2\}$. Although this number system shares several properties with the classical decimal system, it shows remarkable differences and reveals interesting new features. For instance, it is related to the field of $2$-adic numbers, and to some ``fractal'' set that gives rise to a tiling of a non-Euclidean space.

Signal generating circuit and method therefor, and digital time conversion circuit and method therefor

Abstract: A signal generation circuit, a signal generation method, a digital time conversion circuit and a digital time conversion method. The signal generation circuit comprises: a first generation circuit configured to generate a periodic first output signal on the basis of a first frequency control word and a reference time unit, and a second generation circuit configured to generate a periodic second output signal on the basis of a second frequency control word and the reference time unit, wherein the first frequency control word comprises a first integer part and a first decimal part; the second frequency control word comprises a second integer part and a second decimal part; the first integer part is equal to the second integer part; the first decimal part is not equal to the second decimal part; and the period of the first output signal is not equal to the period of the second output signal.