6,204 research outputs found
On the Chow ring of certain rational cohomology tori
Let be an abelian cover from a complex algebraic variety
with quotient singularities to an abelian variety. We show that induces
an isomorphism between the rational cohomology rings
and if and only if induces an isomorphism
between the Chow rings with rational coefficients
and
.Comment: 6 page
Endogenous Business Cycles with Consumption Externalities
Empirical evidences tell us that in the recent years the expansion period is increased with reduction of the contraction period in the U.S. business cycles. Moreover, the business cycles in the United States also show the trend to be moderated with recent economic growth induced and supported by high technologies and their industries. We study endogenous business cycles by a modified synthesized endogenous business cycles model ĂąâŹĆin which expansions are neoclassical growth periods driven by productivity improvements and capital accumulation, while downturns are the results of Keynesian contractions in aggregate demandù⏠(Francois and Lloyd-Ellis, 2002), with consumption externalities. By considering consumption externalities, the endogenized business cycles will be more likely to happen, the optimal consumption level will be higher, the technology growth rate will be bigger, the length of expansion will be longer and the length of contraction will be shorter. All of these results will lead to a faster and longer economic growth and smoother cycles. These theoretical results are significantly different from those in circumstances without the consumption externalities Francois and Lloyd-Ellis (2002) obtained, and are strongly supported by the data from the United States in the different periods.Endogenous Business Cycle, Consumption Externality, Endogenous Growth
Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori
This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin
spaces on a noncommutative -torus (with a
skew symmetric real -matrix). These spaces share many properties
with their classical counterparts. We prove, among other basic properties, the
lifting theorem for all these spaces and a Poincar\'e type inequality for
Sobolev spaces. We also show that the Sobolev space
coincides with the Lipschitz space of order
, already studied by Weaver in the case . We establish the embedding
inequalities of all these spaces, including the Besov and Sobolev embedding
theorems. We obtain Littlewood-Paley type characterizations for Besov and
Triebel-Lizorkin spaces in a general way, as well as the concrete ones in terms
of the Poisson, heat semigroups and differences. Some of them are new even in
the commutative case, for instance, our Poisson semigroup characterizations
improve the classical ones. As a consequence of the characterization of the
Besov spaces by differences, we extend to the quantum setting the recent
results of Bourgain-Br\'ezis -Mironescu and Maz'ya-Shaposhnikova on the limits
of Besov norms. The same characterization implies that the Besov space
for is the quantum
analogue of the usual Zygmund class of order . We investigate the
interpolation of all these spaces, in particular, determine explicitly the
K-functional of the couple , which is the quantum analogue of a classical
result due to Johnen and Scherer. Finally, we show that the completely bounded
Fourier multipliers on all these spaces do not depend on the matrix ,
so coincide with those on the corresponding spaces on the usual -torus
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