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For two sets of strings S 1 and S 2, the concatenation S 1 S 2 consists of all strings of the form vw where v is a string from S 1 and w is a string from S 2, or formally S 1 S 2 = { vw : v ∈ S 1, w ∈ S 2}. Many authors also use concatenation of a string set and a single string, and vice versa, which are defined similarly by S 1 w = { vw ...
Let H be a Hadamard matrix of order n.The transpose of H is closely related to its inverse.In fact: = where I n is the n × n identity matrix and H T is the transpose of H.To see that this is true, notice that the rows of H are all orthogonal vectors over the field of real numbers and each have length .
Propagation of a ray through a layer. The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified medium; a stack of thin films.
The vertical shear displaces points to the right of the y-axis up or down, depending on the sign of m. It leaves vertical lines invariant, but tilts all other lines about the point where they meet the y-axis. Horizontal lines, in particular, get tilted by the shear angle to become lines with slope m.
UNIX Style, or cat -v Considered Harmful - A paper by Rob Pike on proper Unix command design using cat as an example. cat(1) original manual page in the First Edition of Unix: concatenate and write files – GNU Coreutils reference: concatenate and print files – OpenBSD General Commands Manual
Joint All-Domain Command and Control or JADC2 is the concept that the Department of Defense has developed to connect sensors from all branches of the armed forces into a § unified network powered by artificial intelligence. [1] [2] [3] These branches include the Air Force, Army, Marine Corps, and Navy, as well as Space Force.