Step Pyramid Distribution for Prime Numbers

In this document, we will present a new way to visualize the distribution of Prime Numbers in the number system to spot Prime numbers in a subset of numbers using a simpler algorithm. Then we will look throw a classification algorithm to check if a number is prime using only 7 simple arithmetic operations with an algorithm complexity less than or equal to O (7) operations for any number.

Improved Modular Division Implementation with the Akushsky Core Function

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

Challenging Conditions for Gasoline Particulate Filters (GPFs)

The emission limit of non-volatile particles (i.e., particles that do not evaporate at 350 °C) with size >23 nm, in combination with the real driving emissions (RDE) regulation in 2017, resulted in the introduction of gasoline particulate filters (GPFs) in all light-duty vehicles with gasoline direct injection engines in Europe. Even though there are studies that have examined the particulate emissions at or beyond the current RDE boundary conditions, there is a lack of studies combining most or all worst cases (i.e., conditions that increase the emissions). In this study, we challenged a fresh (i.e., no accumulation of soot or ash) “advanced” prototype GPF at different temperatures (down to −9 °C), aggressive drive cycles and hard accelerations (beyond the RDE limits), high payload (up to 90%), use of all auxiliaries (air conditioning, heating of the seats and the rear window), and cold starts independently or simultaneously. Under hot engine conditions, the increase of the particulate emissions due to higher payload and lower ambient temperature was 30–90%. The cold start at low ambient temperature, however, had an effect on the emissions of up to a factor of 20 for particles >23 nm or 300 when considering particles <23 nm. We proposed that the reason for these high emissions was the incomplete combustion and the low efficiency of the three-way oxidation catalyst. This resulted in a high concentration of species that were in the gaseous phase at the high temperature of the close-coupled GPF and thus could not be filtered by the GPF. As the exhaust gas cooled down, these precursor species formed particles that could not be evaporated at 350 °C (the temperature of the particle number system). These results highlight the importance of the proper calibration of the engine out emissions at all conditions, even when a GPF is installed.

Piecewise Structural Equation Modeling of the Quantity Implicature in Child Language

We review an array of experimental methodological factors that either contribute to or detract from the measurement of pragmatic implicatures in child language. We carry out a truth value judgment task to measure children’s interpretations of the Spanish existential quantifier algunos in implicature-consistent and implicature-inconsistent contexts. Independently, we take measures of children’s inhibition, working memory, attention, approximate number ability, phrasal syntax, and lexicon. We model the interplay of these variables using a piecewise structural equation model (SEM), common in the life sciences, but not in the social and behavioral sciences. By 6 years of age, the children in our sample were not statistically different from adults in their interpretations. Syntax, lexicon, and inhibition significantly predict implicature generation, each accounting for unique variance. The approximate number system and inhibition significantly predict lexical development. The statistical power of the piecewise SEM components, with a sample of 64 children, is high, in comparison to a traditional, globally estimated SEM of the same data.

Multiple Error Correction in Redundant Residue Number Systems: A Modified Modular Projection Method with Maximum Likelihood Decoding

Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge number of different possible combinations of erroneous residual digit positions in the error localization stage. This paper proposes a modified correcting method based on calculating the approximate weighted characteristics of modular projections. The new procedure for correcting errors and restoring numbers in a weighted number system involves the Chinese Remainder Theorem with fractions. This approach calculates the rank of each modular projection efficiently. The ranks are used to calculate the Hamming distances. The new method speeds up the procedure for correcting multiple errors and restoring numbers in weighted form by an average of 18% compared to state-of-the-art analogs.

Indigenous Knowledge and the Social Construction of Patriarchy: The Case of the Bukusu of Kenya

This article is an ethnographic study on the Bukusu number system and the connections between Indigenous knowledge and patriarchy. It examines the ways patriarchy is embedded in everyday knowledge through a number system that has deep gender hierarchy symbolisms. The findings show strong connection between everyday knowledge and social norms that define the status of men and women. While this article is centered on Bukusu society in Kenya, it is premised on the understanding that patriarchy is a pervasive social problem that goes beyond Indigenous societies as evident in the feminist critiques of contemporary societies. Just as Durkheim traced the genesis of society to the simplest forms of rules associated with totemic beliefs, this article also points to the roots of patriarchy in Indigenous society so as to draw attention to the variety of ways in which patriarchy is manifested. By incorporating feminist critiques of patriarchy, it shows conceptual connections between the blatant manifestation of patriarchy in Indigenous societies and the latent, albeit oppressive, manifestations of patriarchy in modern societies. Overall, the article provides deep conceptual insights into the intersection of knowledge systems and patriarchy.

The summary lesson on the theme "number systems" in the web quest format

The theme "Number systems" is one of the basic in the school informatics course. The material of this theme is present in the tasks of the Main State Examination and the Unified State Examination, therefore it is very important to timely and efficiently consolidate the basic algorithms to convert numbers from one number system to another. The article provides a variant of such a summary lesson on the theme "Number systems" for the 8th grade in the format of web quest. The quest was developed in the Thinglink environment and contains several locations, each of which is associated with the convertion of numbers between different number systems. The tools for solving the quest tasks are Google Sheets and the LearningApps service, in which the author of the article has developed his own educational resources, as well as the Geogebra environment for performing constructions in one of the tasks. The presented quest can also be carried out in a computer-less form

Zero-Aware Low-Precision RNS Scaling Scheme

Scaling is one of the complex operations in the Residue Number System (RNS). This operation is necessary for RNS-based implementations of deep neural networks (DNNs) to prevent overflow. However, the state-of-the-art RNS scalers for special moduli sets consider the 2k modulo as the scaling factor, which results in a high-precision output with a high area and delay. Therefore, low-precision scaling based on multi-moduli scaling factors should be used to improve performance. However, low-precision scaling for numbers less than the scale factor results in zero output, which makes the subsequent operation result faulty. This paper first presents the formulation and hardware architecture of low-precision RNS scaling for four-moduli sets using new Chinese remainder theorem 2 (New CRT-II) based on a two-moduli scaling factor. Next, the low-precision scaler circuits are reused to achieve a high-precision scaler with the minimum overhead. Therefore, the proposed scaler can detect the zero output after low-precision scaling and then transform low-precision scaled residues to high precision to prevent zero output when the input number is not zero.

A DNA barcode library for the water mites of Montenegro

Water mites (Acari, Hydrachnidia) are a significant component of freshwater ecosystems inhabiting a wide range of aquatic habitats. This study provides a first comprehensive DNA barcode library for the water mites of Montenegro. DNA barcodes were analysed from 233 specimens of water mites morphologically assigned to 86 species from 28 genera and 15 families. In the course of the study, four species, i.e. Lebertia reticulata (Koenike, 1919), Atractides inflatipalpis K.Viets, 1950, A. latipes (Szalay, 1935) and Parabrachypoda montii (Maglio, 1924) were molecularly confirmed as new for Montenegro and three species, i.e. Protzia octopora Lundblad, 1954, Piona laminata (Thor, 1901) and Unionicola ypsilophora (Bonz, 1783) are new for the Balkan Peninsula. Results are analysed using the Barcode Index Number system (BIN) and the Refined Single Linkage (RESL) of BOLD. The BIN assigned sequences to 98 clusters, while the RESL reveal 103 operational taxonomic units (OTUs). Unique BINs were revealed for 72 species (83.7%), whereas twelve species (14%) were characterised by two BINs and two species (2.3%) with three BINs. Amongst the studied taxa, 14 species were found with a high intraspecific sequence divergences (˃ 2.2%), emphasising the need for additional comprehensive morphological and molecu­lar analysis of these species.

Typology of number systems in languages of Western and Central Siberia

This paper investigates the linguistic expression of number in seven languages from Western and Central Siberia. In a first step the number system of each language is described in detail, and afterwards the most relevant convergences and divergences of the languages are dealt with. Three particularly interesting phenomena are discussed in more detail: First, it is shown that the concept of general number, denoting noun forms underspecified for number, is able to account for a range of related phenomena (unmarked noun forms after numerals, nouns denoting paired objects). Second, singulatives in Selkup, Ket and partly Eastern Khanty are analyzed, whereby it is argued that their similar morphosyntactic and grammaticalization patterns allow for analyzing them as a contact phenomenon. Third, two splits on the animacy hierarchy between the first and second person in Dolgan as well as Chulym Turkic are presented. Finally, the results are evaluated against a broader areal-typological background, whereby it is shown that the category of number does not support any larger areal groupings within Western and Central Siberia, but that the analyzed languages rather adhere to patterns of number marking present all over Northern Eurasia.