Differentiability at the tip of Arnold tongues for renormalization group explanations
... more than a century ago, and has been an active area of both theoretical and applied research. Circle maps arise in many other applications (the reader interested in examples of such applications is referred to [PM80, MP84, Gla91, Ign95, dlLP99]). An important topological invariant for circle maps i ...
... more than a century ago, and has been an active area of both theoretical and applied research. Circle maps arise in many other applications (the reader interested in examples of such applications is referred to [PM80, MP84, Gla91, Ign95, dlLP99]). An important topological invariant for circle maps i ...
Unit A502/02 - Sample scheme of work and lesson plan booklet
... Each scheme of work and lesson plan is provided in Word format – so that you can use it as a foundation to build upon and amend the content to suit your teaching style and learners’ needs. This booklet provides examples of how to structure the teaching of this unit; the teaching hours are suggestion ...
... Each scheme of work and lesson plan is provided in Word format – so that you can use it as a foundation to build upon and amend the content to suit your teaching style and learners’ needs. This booklet provides examples of how to structure the teaching of this unit; the teaching hours are suggestion ...
Sequences of Numbers Involved in Unsolved Problems, Hexis, 1990, 2006
... It is based on the old article “Properties of Numbers” (1975), updated many times. Special thanks to C. Dumitrescu & V. Seleacu from the University of Craiova (see their edited book "Some Notions and Questions in Number Theory", Erhus Univ. Press, Glendale, 1994), M. Perez, J. Castillo, M. Bencze, L ...
... It is based on the old article “Properties of Numbers” (1975), updated many times. Special thanks to C. Dumitrescu & V. Seleacu from the University of Craiova (see their edited book "Some Notions and Questions in Number Theory", Erhus Univ. Press, Glendale, 1994), M. Perez, J. Castillo, M. Bencze, L ...
X - University of California, Santa Barbara
... Finite Range Can Lead to Disaster Example: Explosion of Ariane Rocket (1996 June 4) Source http://www.math.psu.edu/dna/455.f96/disasters.html Unmanned Ariane 5 rocket of the European Space Agency veered off its flight path, broke up, and exploded only 30 s after lift-off (altitude of 3700 m) The $5 ...
... Finite Range Can Lead to Disaster Example: Explosion of Ariane Rocket (1996 June 4) Source http://www.math.psu.edu/dna/455.f96/disasters.html Unmanned Ariane 5 rocket of the European Space Agency veered off its flight path, broke up, and exploded only 30 s after lift-off (altitude of 3700 m) The $5 ...
squares and square roots
... In earlier classes, we have studied numbers which can be obtained by raising rational numbers to integral exponents. When the exponent is two, the numbers obtained are called squares or square numbers and the number itself is called the square root of the square so obtained. In this Chapter, we will ...
... In earlier classes, we have studied numbers which can be obtained by raising rational numbers to integral exponents. When the exponent is two, the numbers obtained are called squares or square numbers and the number itself is called the square root of the square so obtained. In this Chapter, we will ...
chap18.pdf
... — Amount of computation for each is similar — Drawback of point-based: If polygon is far from the origin then numerical problems can occur vectors pi and pi +1 will be close to parallel — Advantage of vector-based: intermediate computations meaningful ⇒ Reducing an equation to its “simplest” form no ...
... — Amount of computation for each is similar — Drawback of point-based: If polygon is far from the origin then numerical problems can occur vectors pi and pi +1 will be close to parallel — Advantage of vector-based: intermediate computations meaningful ⇒ Reducing an equation to its “simplest” form no ...
Tutorial_1.1_Solution
... 6) Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. a) -40° Ans: -0.70 radian b) 125° ...
... 6) Convert each angle in degrees to radians. Express your answer in decimal form, rounded to two decimal places. a) -40° Ans: -0.70 radian b) 125° ...
Year 1 Writing
... equal represents regular polygons. The pupil can answer questions such as 'I get to the bus stop at 8:35 a.m. and catch the first bus that arrives. What time do I arrive at Penzance?' by interpreting an appropriate bus timetable. The pupil can complete tables and timetables, deducing what is needed ...
... equal represents regular polygons. The pupil can answer questions such as 'I get to the bus stop at 8:35 a.m. and catch the first bus that arrives. What time do I arrive at Penzance?' by interpreting an appropriate bus timetable. The pupil can complete tables and timetables, deducing what is needed ...
SOLUTIONS TO HOMEWORK 3 1(a).
... If you prefer, this can be rewritten as a0 + 10a1 − a2 − 10a3 + a4 + 10a5 − a6 − 10a7 + · · · . Another possible answer would be the rule for dividing by 41. It divides 99999, and so it also has a simple rule, but with period 5 rather than period 4. 2(a). Find a multiplicative inverse of 17 modulo 1 ...
... If you prefer, this can be rewritten as a0 + 10a1 − a2 − 10a3 + a4 + 10a5 − a6 − 10a7 + · · · . Another possible answer would be the rule for dividing by 41. It divides 99999, and so it also has a simple rule, but with period 5 rather than period 4. 2(a). Find a multiplicative inverse of 17 modulo 1 ...
View - Department of Training and Workforce Development
... the source of the copyright material. The Department of Training and Workforce Development requests attribution as: © Department of Training and Workforce Development (year of publication). Excluded Material not available under a Creative Commons license: 1. The Department of Training and Workforce ...
... the source of the copyright material. The Department of Training and Workforce Development requests attribution as: © Department of Training and Workforce Development (year of publication). Excluded Material not available under a Creative Commons license: 1. The Department of Training and Workforce ...
10/1
... A cylinder 90 cm high has a circumference of 24 cm. A string makes exactly 5 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm? ...
... A cylinder 90 cm high has a circumference of 24 cm. A string makes exactly 5 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm? ...
Chapter 2
... boiling point, freezing point, mass) need to be taken •When these measurements are taken, they are expressed in standard quantities known as units ...
... boiling point, freezing point, mass) need to be taken •When these measurements are taken, they are expressed in standard quantities known as units ...
10/1. There is a number, greater than zero, that is 3 times the sum of
... A cylinder 90 cm high has a circumference of 24 cm. A string makes exactly 5 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm? ...
... A cylinder 90 cm high has a circumference of 24 cm. A string makes exactly 5 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm? ...
On the digital representation of integers with bounded prime factors
... with only the digit 1 in their decimal representation). Both questions are notorious, very difficult open problems, which at present seem to be completely out of reach. However, there have been recently several spectacular advances on the digital representation of prime numbers. In 2010, Mauduit and ...
... with only the digit 1 in their decimal representation). Both questions are notorious, very difficult open problems, which at present seem to be completely out of reach. However, there have been recently several spectacular advances on the digital representation of prime numbers. In 2010, Mauduit and ...
Approximations of π
Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era (Archimedes). In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.Further progress was made only from the 15th century (Jamshīd al-Kāshī), and early modern mathematicians reached an accuracy of 35 digits by the 18th century (Ludolph van Ceulen), and 126 digits by the 19th century (Jurij Vega), surpassing the accuracy required for any conceivable application outside of pure mathematics.The record of manual approximation of π is held by William Shanks, who calculated 527 digits correctly in the years preceding 1873. Since the mid 20th century, approximation of π has been the task of electronic digital computers; the current record (as of May 2015) is at 13.3 trillion digits, calculated in October 2014.