66,823 research outputs found
Mixed integer predictive control and shortest path reformulation
Mixed integer predictive control deals with optimizing integer and real
control variables over a receding horizon. The mixed integer nature of controls
might be a cause of intractability for instances of larger dimensions. To
tackle this little issue, we propose a decomposition method which turns the
original -dimensional problem into indipendent scalar problems of lot
sizing form. Each scalar problem is then reformulated as a shortest path one
and solved through linear programming over a receding horizon. This last
reformulation step mirrors a standard procedure in mixed integer programming.
The approximation introduced by the decomposition can be lowered if we operate
in accordance with the predictive control technique: i) optimize controls over
the horizon ii) apply the first control iii) provide measurement updates of
other states and repeat the procedure
Loop group actions on categories and Whittaker invariants
We develop some aspects of the theory of -modules on ind-schemes of
pro-finite type. These notions are used to define -modules on (algebraic)
loop groups and, consequently, actions of loop groups on DG categories.
Let be the maximal unipotent subgroup of a reductive group . For a
non-degenerate character and a category
acted upon by , we define the category
of -invariant objects,
along with the coinvariant category . These are
the Whittaker categories of , which are in general not equivalent.
However, there is always a family of functors ,
parametrized by .
We conjecture that each is an equivalence, provided that the
-action on extends to a -action. Using
the Fourier-Deligne transform (adapted to Tate vector spaces), we prove this
conjecture for and show that the Whittaker categories can be obtained
by taking invariants of with respect to a very explicit
pro-unipotent group subscheme (not ind-scheme) of
BV-regularity for the Malliavin Derivative of the Maximum of the Wiener Process
We prove that, on the classical Wiener space, the random variable admits a measure as second Malliavin derivative, whose total
variation measure is finite and singular w.r.t.\ the Wiener measure
Zero noise limits using local times
We consider a well-known family of SDEs with irregular drifts and the
correspondent zero noise limits. Using (mollified) local times, we show which
trajectories are selected. The approach is completely probabilistic and relies
on elementary stochastic calculus only
Oscillating shells: A model for a variable cosmic object
A model for a possible variable cosmic object is presented. The model
consists of a massive shell surrounding a compact object. The gravitational and
self-gravitational forces tend to collapse the shell, but the internal
tangential stresses oppose the collapse. The combined action of the two types
of forces is studied and several cases are presented. In particular, we
investigate the spherically symmetric case in which the shell oscillates
radially around a central compact object
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