6,660 research outputs found
Harder-Narasimhan Filtrations and K-Groups of an Elliptic Curve
Let be an elliptic curve over an algebraically closed field. We prove
that some exact sub-categories of the category of vector bundles over ,
defined using Harder-Narasimhan filtrations, have the same K-groups as the
whole category.Comment: 5 pages, typos correcte
On the Vertices of Indecomposable Modules Over Dihedral 2-Groups
Let be an algebraically closed field of characteristic 2. We compute the
vertices of all indecomposable -modules for the dihedral group of
order 8. We also give a conjectural formula of the induced module of a string
module from to where is a dihedral group of order and
where is a dihedral subgroup of index 2 of . Some cases where we
verified this formula are given.Comment: 19 page
Kuelshammer ideals and the scalar problem for blocks with dihedral defect groups
In by now classical work, K. Erdmann classified blocks of finite groups with
dihedral defect groups (and more generally algebras of dihedral type) up to
Morita equivalence. In the explicit description by quivers and relations of
such algebras with two simple modules, several subtle problems about scalars
occurring in relations remained unresolved. In particular, for the dihedral
case it is a longstanding open question whether blocks of finite groups can
occur for both possible scalars 0 and 1. In this article, using Kuelshammer
ideals (a.k.a. generalized Reynolds ideals), we provide the first examples of
blocks where the scalar is 1, thus answering the above question to the
affirmative. Our examples are the principal blocks of PGL_2(F_q), the
projective general linear group of 2x2-matrices with entries in the finite
field F_q, where q=p^n\equiv \pm 1 mod 8, with p an odd prime number.Comment: 23 page
Auslander-Reiten conjecture for symmetric algebras of polynomial growth
This paper studies self-injective algebras of polynomial growth. We prove
that the derived equivalence classification of weakly symmetric algebras of
domestic type coincides with the classification up to stable equivalences (of
Morita type). As for weakly symmetric non-domestic algebras of polynomial
growth, up to some scalar problems, the derived equivalence classification
coincides with the classification up to stable equivalences of Morita type. As
a consequence, we get the validity of the Auslander-Reiten conjecture for
stable equivalences of Morita type between weakly symmetric algebras of
polynomial growth
Numerical approximations of the Cahn-Hilliard and Allen-Cahn Equations with general nonlinear potential using the Invariant Energy Quadratization approach
In this paper, we carry out stability and error analyses for two first-order,
semi-discrete time stepping schemes, which are based on the newly developed
Invariant Energy Quadratization approach, for solving the well-known
Cahn-Hilliard and Allen-Cahn equations with general nonlinear bulk potentials.
Some reasonable sufficient conditions about boundedness and continuity of the
nonlinear functional are given in order to obtain optimal error estimates.
These conditions are naturally satisfied by two commonly used nonlinear
potentials including the double-well potential and regularized logarithmic
Flory-Huggins potential. The well-posedness, unconditional energy stabilities
and optimal error estimates of the numerical schemes are proved rigorously
Verdier quotients of homotopy categories
We study Verdier quotients of diverse homotopy categories of a full additive
subcategory of an abelian category. In particular, we consider the
categories for , and
the homotopy categories of left, right,
unbounded complexes with homology being , bounded, left or right bounded, or
unbounded. Inclusion of these categories give a partially ordered set, and we
study localisation sequences or recollement diagrams between the Verdier
quotients, and prove that many quotients lead to equivalent categories
Ergodic Diffusion Control of Multiclass Multi-Pool Networks in the Halfin-Whitt Regime
We consider Markovian multiclass multi-pool networks with heterogeneous
server pools, each consisting of many statistically identical parallel servers,
where the bipartite graph of customer classes and server pools forms a tree.
Customers form their own queue and are served in the first-come first-served
discipline, and can abandon while waiting in queue. Service rates are both
class and pool dependent. The objective is to study the limiting diffusion
control problems under the long run average (ergodic) cost criteria in the
Halfin--Whitt regime. Two formulations of ergodic diffusion control problems
are considered: (i) both queueing and idleness costs are minimized, and (ii)
only the queueing cost is minimized while a constraint is imposed upon the
idleness of all server pools. We develop a recursive leaf elimination algorithm
that enables us to obtain an explicit representation of the drift for the
controlled diffusions. Consequently, we show that for the limiting controlled
diffusions, there always exists a stationary Markov control under which the
diffusion process is geometrically ergodic. The framework developed in our
earlier work is extended to address a broad class of ergodic diffusion control
problems with constraints. We show that that the unconstrained and constrained
problems are well posed, and we characterize the optimal stationary Markov
controls via HJB equations.Comment: 32 page
Existence of steady multiple vortex patches to the vortex-wave system
In this paper we prove the existence of steady multiple vortex patch
solutions to the vortex-wave system in a planar bounded domain. The
construction is performed by solving a certain variational problem for the
vorticity and studying its asymptotic behavior as the vorticity strength goes
to infinity.Comment: 22 page
Steady double vortex patches with opposite signs in a planar ideal fluid
In this paper we consider steady vortex flows for the incompressible Euler
equations in a planar bounded domain. By solving a variational problem for the
vorticity, we construct steady double vortex patches with opposite signs
concentrating at a strict local minimum point of the Kirchhoff-Routh function
with . Moreover, we show that such steady solutions are in fact local
maximizers of the kinetic energy among isovortical patches, which correlates
stability to uniqueness.Comment: 17 page
Golden-rule capacity allocation for distributed delay management in peer-to-peer networks
We describe a distributed framework for resources management in peer-to-peer
networks leading to golden-rule reciprocity, a kind of one-versus-rest
tit-for-tat, so that the delays experienced by any given peer's messages in the
rest of the network are proportional to those experienced by others' messages
at that peer
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