Comments on real tachyon vacuum solution without square roots

Rolling Tachyon Solution in Vacuum String Field Theory

We construct a time-dependent solution in vacuum string field theory and investigate whether the solution can be regarded as a rolling tachyon solution. First, compactifying one space direction on a circle of radius R, we construct a spacedependent solution given as an infinite number of ∗-products of a string field with center-of-mass momentum dependence of the form e 2/4. Our time-dependent s...

On taking square roots without quadratic nonresidues over finite fields

We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and the proof is elementary. In some cases, the square root algorithm runs in Õ(log q) bit operations over finite fields with q elements. As an application, we construct a deterministic primality-proving al...

Logarithms and Square Roots of Real Matrices

The need for computing logarithms or square roots of real matrices arises in a number of applied problems. A significant class of problems comes from medical imaging. One of these problems is to interpolate and to perform statistics on data represented by certain kinds of matrices (such as symmetric positive definite matrices in DTI). Another important and difficult problem is the registration ...

On computing complex square roots of real matrices

We present an idea for computing complex square roots of matrices using only real arithmetic.

On group Elements Having Square Roots