s . so c - ph ] 1 1 Ju l 2 00 6 Virtual volatility

s . so c - ph ] 2 1 N ov 2 00 6 Virtual volatility

We introduce the concept of virtual volatility. This simple but new measure shows how to quantify the uncertainty in the forecast of the drift component of a random walk. The virtual volatility also is a useful tool in understanding the stochastic process for a given portfolio. In particular, and as an example, we were able to identify mean reversion effect in our portfolio. Finally, we briefly...

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications

ar X iv : m at h - ph / 0 10 70 08 v 1 1 0 Ju l 2 00 1 Prelle - Singer Approach and Liouvillian Solutions : An Important Result

In [1], we present a method to tackle first order ordinary differential equations whose solutions contain Liouvillian functions (LFOODEs), many of them missed by the usual PS-approach. Here, we demonstrate an important result concerning the generality of that method.

ar X iv : m at h - ph / 0 60 80 01 v 1 3 1 Ju l 2 00 6 1 Modular Invariants and Fischer - Griess Monster 1

We show interesting relations between extremal partition functions of a family of conformal field theories and dimensions of the irreducible representations of the Fischer-Griess Monster sporadic group. We argue that these relations can be interpreted as an extension of Monster moonshine.

ar X iv : 0 90 6 . 12 19 v 2 [ ph ys ic s . at om - p h ] 2 5 Ju l 2 00 9 Spin - 1 / 2 Optical Lattice Clock

We experimentally investigate an optical clock based on Yb (I = 1/2) atoms confined in an optical lattice. We have evaluated all known frequency shifts to the clock transition, including a densitydependent collision shift, with a fractional uncertainty of 3.4 × 10, limited principally by uncertainty in the blackbody radiation Stark shift. We measured the absolute clock transition frequency rela...