Assessment of Rational Number Understanding: A Schema-Based Approach: Sandra P. Marshall

2012 ◽  
pp. 271-298
Keyword(s):  
Rational Number ◽  
Rational Number Understanding

Spontaneous focusing on quantitative relations as a predictor of the development of rational number conceptual knowledge.

2016 ◽  
Vol 108 (6) ◽  
pp. 857-868 ◽  
Author(s):  
Jake McMullen ◽  
Minna M. Hannula-Sormunen ◽  
Eero Laakkonen ◽  
Erno Lehtinen
Keyword(s):  
Rational Number ◽  
Conceptual Knowledge

STRUCTURAL AND LOGIC DIAGRAM OF RESEARCH ON THE MILITARY-ECONOMIC SUBSTANTIATION OF THE RATIONAL NUMBER OF ARMED FORCES OF UKRAINE IN THE PROCESS OF FORMING THE PROGRAM OF THEIR DEVELOPMENT

2019 ◽  
Vol 2 (12) ◽  
pp. 102-110
Author(s):  
V. Nazarkin ◽  
O. Semenenko ◽  
A. Efimenko ◽  
V. Ivanov
Keyword(s):  
Rational Number ◽  
Armed Forces ◽  
The State ◽  
Limiting Factors ◽  
Development Programs ◽  
Power Structures ◽  
Scientific Substantiation ◽  
Conducting Research ◽  
Excess Number ◽  
The Military

The task of choosing the rational number of power structures is always one of the main priorities of any political leadership of the state. An insufficient number of armed forces is a threat to the national security of the state; an excess number creates pressures on the development of the country's national economy. Today, when the development programs of the Armed Forces of Ukraine are being formed in the context of the practical application of their units and subunits to carry out combat missions, questions of choosing a priority approach to the formation (justification) of the rational size of the Armed Forces of Ukraine is an urgent issue. The article proposes a structure for conducting research on the development and implementation of the methodology of military-economic substantiation of the rational strength of the Armed Forces of Ukraine in the system of defense planning of Ukraine in the formation of programs for their development for the medium and long term. The main objectives of this methodology are: scientific substantiation of the range of the necessary strength of the Armed Forces of Ukraine for the period of the program of their development; the choice of the indicator of the rational size of the Armed Forces of Ukraine according to the years of the program from a certain range of its changes; military-economic substantiation of this number under the influence of various limiting factors. The development and implementation of such a methodology will increase the efficiency of the formation and implementation of development programs of the Armed Forces of Ukraine, as well as the efficiency of using public funds for the development of power structures.

scholarly journals On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
WonTae Hwang ◽  
Kyunghwan Song
Keyword(s):  
Zeta Function ◽  
Rational Number ◽  
Riemann Zeta Function ◽  
Rational Numbers ◽  
Critical Strip ◽  
Integer Part ◽  
Integral Points ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Abstract We prove that the integer part of the reciprocal of the tail of $\zeta (s)$ ζ ( s ) at a rational number $s=\frac{1}{p}$ s = 1 p for any integer with $p \geq 5$ p ≥ 5 or $s=\frac{2}{p}$ s = 2 p for any odd integer with $p \geq 5$ p ≥ 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\frac{2}{p}$ s = 2 p , we use a result on the finiteness of integral points of certain curves over $\mathbb{Q}$ Q .

scholarly journals Acceleration of Euclidean Algorithm and Rational Number Reconstruction

2003 ◽  
Vol 32 (2) ◽  
pp. 548-556 ◽  
Author(s):  
Xinmao Wang ◽  
Victor Y. Pan
Keyword(s):  
Rational Number ◽  
Euclidean Algorithm

scholarly journals ON -K2 FOR NORMAL SURFACE SINGULARITIES

1998 ◽  
Vol 09 (06) ◽  
pp. 653-668 ◽  
Author(s):  
HAO CHEN ◽  
SHIHOKO ISHII
Keyword(s):  
Lower Bound ◽  
Positive Integer ◽  
Rational Number ◽  
Accumulation Point ◽  
Normal Surface ◽  
Accumulation Points ◽  
Surface Singularities

In this paper we show the lower bound of the set of non-zero -K2 for normal surface singularities establishing that this set has no accumulation points from above. We also prove that every accumulation point from below is a rational number and every positive integer is an accumulation point. Every rational number can be an accumulation point modulo ℤ. We determine all accumulation points in [0, 1]. If we fix the value -K2, then the values of pg, pa, mult, embdim and the numerical indices are bounded, while the numbers of the exceptional curves are not bounded.

Call for Manuscripts for the 2014 Focus Issue: Rational Number Sense – October 2012

2012 ◽  
Vol 18 (3) ◽  
pp. 189
Keyword(s):  
Rational Number ◽  
Number Sense ◽  
Rational Numbers

This call for manuscripts is requesting articles that address how to make sense of rational numbers in their myriad forms, including as fractions, ratios, rates, percentages, and decimals.

scholarly journals Distribution of rational points on the real line

1973 ◽  
Vol 15 (2) ◽  
pp. 243-256 ◽  
Author(s):  
T. K. Sheng
Keyword(s):  
Algebraic Number ◽  
Rational Number ◽  
Real Line ◽  
Rational Points ◽  
The Other ◽  
Liouville Numbers ◽  
The Real ◽  
Other Hand ◽  
Image Position

It is well known that no rational number is approximable to order higher than 1. Roth [3] showed that an algebraic number is not approximable to order greater than 2. On the other hand it is easy to construct numbers, the Liouville numbers, which are approximable to any order (see [2], p. 162). We are led to the question, “Let Nn(α, β) denote the number of distinct rational points with denominators ≦ n contained in an interval (α, β). What is the behaviour of Nn(α, + 1/n) as α varies on the real line?” We shall prove that and that there are “compressions” and “rarefactions” of rational points on the real line.

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