This book introduces the so-called “stable factorization approach” to the synthesis of feedback controllers for linear control systems. The key to this approach is to view the multi-input, multi-output (MIMO) plant for which one wishes to design a controller as a matrix over the fraction field F associated with a commutative ring with identity, denoted by R, which also has no divisors of zero. 229 more words

## Tags » Factorization

#### Prime Number Problem

Following is a problem about prime factorization of the sum of consecutive odd primes. (source: problem 80 from The Green Book of Mathematical Problems) 211 more words

#### Fast and slow machines

In my previous post, I presented three hypothetical *machines* which take a positive integer as input and give us something else as output:

#### A tale of three machines

The Fundamental Theorem of Arithmetic tells us that any positive integer can be factored into a product of prime factors.1 Given a positive integer , this leads naturally to several questions: 935 more words

#### Our latest paper: "Factorization and criticality in finite interacting spin systems under a nonuniform magnetic field"

Our latest paper just got published by Physical Review Letter! Let me briefly explain what our manuscript is about: