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Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of rational number arithmetic: inherent and culturally contingent. Inherent sources of difficulty are ones that are imposed by the task of learning rational number arithmetic, such as complex relations among fraction arithmetic operations. They are present for all learners. Culturally contingent sources of difficulty are ones that vary among cultures, such as teacher understanding of rational numbers. They lead to poorer learning among students in some places rather than others. We conclude by discussing interventions that can improve learning of rational number arithmetic.

A Handbook of History, Theory and Practice of the Dewey Decimal Classification System is a comprehensive, practical guide to today's DDC, used by over 200,000 libraries globally. It is an essential companion for DDC classifiers, and reference for students and educators of classification.

In this paper, it is given a generalization of the relation of the repeating decimals which displays the successive terms of the Fibonacci sequence and Pascal's rows. Additionally, two types of fractions that contain successive terms of the Padovan sequence in their decimal representation are given, by reading from left to right and giving numerical illustrations.

In this note, we consider a constant c related to the Glaisher-Kinkelin constant, obtained by a shift of the infinite system of Equations for the Li-Keiper coefficients and related to the Euler formula at s = 2, i.e. ζ(2) = π2/6 for the Zeta function. The aim of the experiment we are carrying out is to relate the Primes with the tiny part (the fluctuations) of the Li-Keiper coefficients as well as with the trend part of them. The contribution of the series for the tiny part or for the trend part are thus related to a series for the primes and we obtain in this ways a upper and a lower bound of the constant c, which will be given with some decimals. Other relations may be obtained along the same lines and additional examples are given.

We aim to tackle the longstanding debate on whether stock liquidity enhances or impedes firm innovation. This topic is of interest because innovation is crucial for firm- and national-level competitiveness and stock liquidity can be altered by financial market regulations. Using a difference-in-differences approach that relies on the exogenous variation in liquidity generated by regulatory changes, we find that an increase in liquidity causes a reduction in future innovation. We identify two possible mechanisms through which liquidity impedes innovation: increased exposure to hostile takeovers and higher presence of institutional investors who do not actively gather information or monitor.

This paper proposes a parallel digital image encryption algorithm based on a piecewise linear chaotic map (PWLCM) and a four-dimensional hyper-chaotic map (FDHCM). Firstly, two decimals are obtained based on the plain-image and external keys, using a novel parallel quantification method. They are used as the initial value and control parameter for the PWLCM. Then, an encryption matrix and four chaotic sequences are constructed using the PWLCM and FDHCM, which control the permutation and diffusion processes. The proposed algorithm is implemented and tested in parallel based on a graphics processing unit device. Numerical analysis and experimental results show that the proposed algorithm achieves a high encryption speed and a good security performance, which provides a potential solution for real-time image encryption applications.

The Dewey Decimal Classification system (DDC) is the world's most popular library classification system.The 23rd edition of the DDC was published in 2011.This second edition of The Theory and Practice of the Dewey Decimal Classification System examines the history, management and technical aspects of the DDC up to its latest edition.

It's crystal clear that presenting a new structure with the aim of decreasing the size of circuits is really vital. So, this paper presents a novel 4-input gate that can give AND, OR, NAND, NOR, and inverter gates with just one structure. The proposed gate utilizes fewer cells to decrease the complexity and of course, the size of circuits. Three different converters including decimal to excess-3, decimal to BCD, and decimal to gray is presented because converters play a crucial role in the electronic world. In the suggested designs the novel 4-input gate is utilized to optimize circuits as much as possible. The utilization of the QCADesigner simulation tool showcases the superiority of the suggested arrangement when compared to previous designs. This assessment is based on evaluating the number of cells utilized, the space occupied, and the latency as key design metrics. For instance, the proposed decimal to BCD converter exhibits a reduction of 22.22% in occupied space and a significant decrease of 7.24% in the number of cells compared to the most similar and newest counterpart scalable designs. Due to the proposed novel gate's advantageous performance across multiple measurement parameters, it can be effectively utilized in larger and more complex circuits.

To evaluate the incidence of Acanthamoeba keratitis in the Netherlands between 2009 and 2015 and to analyse predicting factors for treatment outcome. Patient characteristics, diagnostic methods, diagnostic delay, therapy prior to and after diagnosis, and visual outcome were obtained from medical files of all patients diagnosed with Acanthamoeba keratitis in the Netherlands between 2009 and 2015. A logistic regression analysis on treatment failure, defined as a best corrected visual acuity of less than 20/40 Snellen decimals (i.e. >0.3 logMAR or an approximate loss of three lines of visual acuity) and/or the need for keratoplasty, was performed to determine predicting factors. Two hundred and twenty-four eyes of 224 patients were included. Ninety-five percent of the patients were contact lens wearers, of whom 74% wore soft contact lenses. The number of cases increased from 16 in 2009 to 49 in 2015. This resulted in an estimated incidence of 1 in 21,000 for soft contact lens wearers in 2015. Eighty-seven eyes (39%) met the criteria for treatment failure. In a multivariable regression analysis, higher age at presentation, a higher severity stage and corticosteroid use before diagnosis were positively correlated with treatment failure. Early referral to a cornea specialist was associated with better clinical outcomes. Although Acanthamoeba keratitis is still a relatively uncommon disease, the incidence in soft contact lens wearers has increased to reach 1 in 21,000 in 2015. Treatment failure occurred in 39% of cases, with age, higher severity stage, corticosteroid use before diagnosis and indirect referral to a cornea specialist as important risks factors.