29,627 research outputs found
Effects of an intermediate scale in SUSY grand unification
We discuss the production of lepton flavor violation and EDMs and the
viability of the unification hypothesis in SUSY grand unification with
an intermediate gauge symmetry breaking scale.Comment: 3 pages (Latex, esprc2.sty used), talk given at 4th International
Conference on Supersymmetry (SUSY '96, College Park, MD, May 29 - June 1,
1996
Crossed S-matrices and Character Sheaves on Unipotent Groups
Let be an algebraic closure of a finite field
of characteristic . Let be a connected unipotent group over
equipped with an -structure given by a Frobenius map .
We will denote the corresponding algebraic group defined over by
. Character sheaves on are certain objects in the triangulated braided
monoidal category of bounded conjugation equivariant
-complexes (where is a prime number) on .
Boyarchenko has proved that the "trace of Frobenius" functions associated with
-stable character sheaves on form an orthonormal basis of the space of
class functions on and that the matrix relating this basis
to the basis formed by the irreducible characters of is
block diagonal with "small" blocks. In this paper we describe these block
matrices and interpret them as certain "crossed -matrices". We also derive a
formula for the dimensions of the irreducible representations of
that correspond to one such block in terms of certain
modular categorical data associated with that block. In fact we will formulate
and prove more general results which hold for possibly disconnected groups
such that is unipotent. To prove our results, we will establish a
formula (which holds for any algebraic group ) which expresses the inner
product of the "trace of Frobenius" function of any -stable object of
with any character of (or of any of its
pure inner forms) in terms of certain categorical operations.Comment: 37 pages. Added a section about certain Grothendieck rings. Added
some example
On the role of F\"ollmer-Schweizer minimal martingale measure in Risk Sensitive control Asset Management
Kuroda and Nagai \cite{KN} state that the factor process in the Risk
Sensitive control Asset Management (RSCAM) is stable under the
F\"ollmer-Schweizer minimal martingale measure . Fleming and Sheu \cite{FS} and
more recently F\"ollmer and Schweizer \cite{FoS} have observed that the role of
the minimal martingale measure in this portfolio optimization is yet to be
established. In this article we aim to address this question by explicitly
connecting the optimal wealth allocation to the minimal martingale measure. We
achieve this by using a "trick" of observing this problem in the context of
model uncertainty via a two person zero sum stochastic differential game
between the investor and an antagonistic market that provides a probability
measure. We obtain some startling insights. Firstly, if short-selling is not
permitted and if the factor process evolves under the minimal martingale
measure then the investor's optimal strategy can only be to invest in the
riskless asset (i.e. the no-regret strategy). Secondly, if the factor process
and the stock price process have independent noise, then even if the market
allows short selling, the optimal strategy for the investor must be the
no-regret strategy while the factor process will evolve under the minimal
martingale measure .Comment: A.Deshpande (2015), On the role of F\"ollmer-Schweizer minimal
martingale measure in Risk Sensitive control Asset Management,Vol. 52, No. 3,
Journal of Applied Probabilit
Natural convection in a cubical cavity: Case of multiple solutions
The purpose of this report is to study an interesting case of natural convection13; in a cubical cavity. A set of boundary conditions has been applied on the six walls and13; the buoyancy driven xB0;ow inside the cavity is due to the heating of the bottom wall.13; Interestingly two families of distinct steady solutions have been observed. Both the13; families have the same critical Rayleigh number (Ra)crit below which there is no xB0;ow13; and heat transfer is by pure conduction
- …