Internal Polarization and Relativistic Elementary-Particle Algebra

Particle Acceleration at Multiple Internal Relativistic Shocks

Relativistic shocks provide an efficient method for high-energy particle acceleration in many astrophysical sources. Multiple shock systems are even more effective and of importance, for example, in the internal shock model of gamma-ray bursts. We investigate the reacceleration of pre-existing energetic particles at such relativistic internal shocks by the first order Fermi process of pitch ang...

Particle Acceleration at Multiple Internal Relativistic Shocks 3

Relativistic shocks provide an efficient method for high-energy particle acceleration in many astrophysical sources. Multiple shock systems are even more effective and of importance, for example, in the internal shock model of gamma-ray bursts. We investigate the reacceleration of pre-existing energetic particles at such relativistic internal shocks by the first order Fermi process of pitch ang...

Modular Arithmetic and Elementary Algebra

where z is an integer then gcd(a, b) = gcd(b, c). Indeed any divisor of a and b will divide c, and conversely any divisor of b and c will divide a. We can compute c by taking the remainder after dividing a by b, i.e. c is a mod b. (We will discuss the mod operation in greater details in the next section, but at this point, we only need the definition of c as the remainder of dividing a by b.) B...

Elementary Linear Algebra

Elementary Microarchitecture Algebra

We describe a set of remarkably simple algebraic laws governing microarchitectural components. We apply these laws to incrementally transform a pipeline containing forwarding, branch speculation and hazard detection so that all pipeline stages and forwarding logic are removed. The resulting unpipelined machine is much closer to the reference architecture, and presumably easier to verify.