This latter fact has a precise formulation, known as the Vinogradov mean value theorem, and its proof is the most difficult part of the argument, relying on using a “-adic” version of this equidistribution to reduce the claim at a given scale to a smaller scale with , and then ...
Note that if is reducible but is itself defined over , then the Frobenius endomorphism preserves itself, but may permute the components of around. In this case, is the number of fixed points of this permutation action of Frobenius on the components. In particular, is always a natural number ...
Are permutations part of combinatorics? Does "repetition" mean the same thing as "order" in the context of permutation problems? How many combinations can you make with the numbers 1,2, and 3? How many distinguishable permutations of the letters in the word "possibilities" are there...
What Does FTP Mean in a Text?home▸search f▸FTPThe Quick Answer The abbreviation FTP means "File Transfer Protocol" (in computing), "Free To Play" (in gaming), and "Functional Threshold Power" (in cycling). It also means "F*ck The Police" and "F*ck The Pope" ...
Do any of those have the same relative ordering as Y? No! None of them start at the lowest, go to the middle, then go to the highest. So this time X does not contain Y, so we say that X avoids Y.So What?So now that we know what "X contains Y" and "X avoids Y" mean, ...
randomly permutes the values of the arguments. CALL SCAN returns the position and length of a given word in a character expression. CALL SCANQ returns the position and length of a given word in a character expression, and ignores delimiters that are enclosed in quotation marks. ...
They let me explore designs with shape schemas like Goethe's Urpflanze, too – but perhaps more generally, because organs (unit parts: atoms, bits, building blocks, cells, components, constituents, etc.) aren't predefined to permute and transform. The rules in my schemas use embedding to ...
The nature of theseword puzzle gamesis mathematical. Let us say, there are 80 ways to permute the letters. In a four-letter word without repeated letters, there are 64 possible three-letter words in a 4 by 4 grid of letters. So, a complete mathematical approach is used to construct thes...
Does it mean that we don't need a normal assumption for using sandwich estimator in normal linear regression? Constructing equilateral triangle with a vertex on approximately lattice points An almost steam-punk short fiction about robot childcarers How to permute p-values? Dec...
In Remark 7.1.3, it says, “In particular, one can replace the index of summation with any other symbol, and obtain the same sum.” Does this really mean any symbol? Can one replace with if is a fixed integer and doesn’t refer to any fixed quantity? Reply 6...