![]() You want to show there are functions f that equal 0 on one side of a closed interval and equal 1 on the other side. One of the steps along the way is to prove that you can create functions than ramp up smoothly between constant values. Proving the existence of partitions of unity with the desired properties isn’t trivial. The functions are chosen to have properties that let you glue together local results to create a global result. ![]() The functions split up (partition) the number 1 (unity) at each point. A partition of unity is a set of smooth functions into the interval that add up to 1 at every point. The name sounds odd, but it’s descriptive. They’re seldom the focus of attention but rather are buried in the middle of proofs. Partitions of unity are a handy technical device. Others, are pairs that of valid words but not the same word, such as ail and fin. Some of these words remain the same when translated to Morse, reversed, and translated back, such as sans. But there are no Morse palindromes in French if you add ü. As far as I know, there are no codes for accented letters which are valid letters when reversed, except for ü whose code is the opposite of z. The code for é is itself a palindrome, so I didn’t need to modify my script for it. ![]() It’s not clear exactly what is “French Morse code” because there are a number of code values that could be used in French (or English) to represent letters with diacritical marks. I thought I’d have to modify the script because French uses characters in addition to the 26 letters of the Roman alphabet, such as ç, a ‘c’ with a cedilla. Now what about French? I saved the script I wrote to find Morse palindromes in English, and I ran it on the French dictionary located at /usr/share/dict The word wig is a palindrome in Morse code because. The word kayak is not a Morse code palindrome because its Morse code representation. ![]() A Morse code palindrome is a word that remains the same when its Morse code representation is reversed. PalindromesĪ palindrome is a word that remains the same when the letters are reversed, like kayak. I got an email from a student in France who asked about a French counterpart to my post on Morse code palindromes, and this post is a response to that email. So pull off all the symbols you can from the beginning of the list of dots and dashes and in each case recurse on the rest of the list. ) added to the front of all sequences that start with. So for the first bullet point, for example, how would we find all sequences that start with. Y ( -.-) added to the front of all sequences that start with.K ( -.-) added to the front of all sequences that start with.N ( -.) added to the front of all sequences that start with.T ( -) added to the front of all sequences that start with.In our case the possible symbols are T, N, K, and Y. Start at the beginning and list the possible symbols formed by consecutive dots and dashes. Here’s an outline of a recursive algorithm to enumerate the possibilities. There are many other ways to parse. So the way I hear “YYX” would be more like “NÖŠI”. There is no symbol corresponding to - either. Using that definition of Morse code, there are no symbols corresponding to. The American amateur radio community defines Morse code as 40 characters: the 26 letters of the Latin alphabet, 10 digits, and 4 more symbols: / =. Interpreting the other groupings depends on what you mean by Morse code. So I hear the 20/8 time signature as (3 + 7 + 10)/8. ![]() My mind splits up the rhythm with each sequence of long notes starting a group:. When I listen to the song, I don’t hear YYZ. Here’s what the opening riff would look like in sheet music:Įach dash is a middle C and each dot is an F# a tritone below middle C. However, the song puts no spaces between rhythm corresponding to each letter. The idea for the song came from hearing the airport identifier in Morse code. YYZ is the designation for the Toronto Pearson International Airport, the main airport serving Toronto. The song YYZ by Rush opens with a theme based on the rhythm of “YYZ” in Morse code:. ![]()
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