1,023 research outputs found
On the finiteness and stability of certain sets of associated primes ideals of local cohomology modules
Let be a Noetherian local ring, an ideal of and a
finitely generated -module. Let be an integer and
r=\depth_k(I,N) the length of a maximal -sequence in dimension in
defined by M. Brodmann and L. T. Nhan ({Comm. Algebra, 36 (2008), 1527-1536).
For a subset S\subseteq \Spec R we set S_{{\ge}k}={\p\in
S\mid\dim(R/\p){\ge}k}. We first prove in this paper that
\Ass_R(H^j_I(N))_{\ge k} is a finite set for all }. Let
\fN=\oplus_{n\ge 0}N_n be a finitely generated graded \fR-module, where
\fR is a finitely generated standard graded algebra over . Let be
the eventual value of \depth_k(I,N_n). Then our second result says that for
all the sets \bigcup_{j{\le}l}\Ass_R(H^j_I(N_n))_{{\ge}k} are
stable for large .Comment: To appear in Communication in Algebr
On the cofiniteness of generalized local cohomology modules
Let be a commutative Noetherian ring, an ideal of and ,
two finitely generated -modules. The aim of this paper is to investigate the
-cofiniteness of generalized local cohomology modules \displaystyle
H^j_I(M,N)=\dlim\Ext^j_R(M/I^nM,N) of and with respect to . We
first prove that if is a principal ideal then is -cofinite
for all and all . Secondly, let be a non-negative integer such
that \dim\Supp(H^j_I(M,N))\le 1 \text{for all} j Then is
-cofinite for all and \Hom(R/I,H^t_I(M,N)) is finitely generated.
Finally, we show that if or then is
-cofinite for all .Comment: 16 page
Generalized Differentiation and Characterizations for Differentiability of Infimal Convolutions
This paper is devoted to the study of generalized differentiation properties
of the infimal convolution. This class of functions covers a large spectrum of
nonsmooth functions well known in the literature. The subdifferential formulas
obtained unify several known results and allow us to characterize the
differentiability of the infimal convolution which plays an important role in
variational analysis and optimization
Existence of competitive equilibrium in a single-sector growth model with heterogeneous agents and endogenous leisure
We prove the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents and elastic labor supply. The method of proof relies on exploiting the existence of Lagrange multipliers in infinite dimensional spaces and the link between Pareto-optima and competitive equilibria.Optimal growth model, Lagrange multipliers, single-sector growth model, competitive equilibrium, elastic labor supply.
Existence of competitive equilibrium in an optimal growth model with heterogeneous agents and endogenous leisure
No-arbitrage condition and existence of equilibrium with dividends
In this paper we first give an elementary proof of existence of equilibrium with dividends in an economy with possibly satiated consumers.We then introduce a no-arbitrage condition and show that it is equivalent to the existence of equilibrium with dividends.equilibrium with dividends, economy with possibly satiated consumers, no-arbitrage condition
Endogenous Fiscal Policies, Environmental Quality, and Status-Seeking Behavior.
This paper analyzes endogenous fiscal policy and public decision in an endogenous growth model where agents care about social status and environmental quality. The quest for a higher status is assimilated to a preference for capital wealth. The government uses income tax to finance infrastructure and environmental protection, and maximizes individual welfare. We find that accounting for preferences for social status and environmental quality may lead to an allocation of tax revenue in favor of cleanup effort to the detriment of infrastructure. It does not necessary have a negative impact on growth. Status seeking can however harm economic growth and environmental quality when its motive is important enough. Finally, we show that economic growth is consistent with environmental preservation but is not necessarily welfare-improving as in the case of absence of status-seeking behavior.Endogenous policy; endogenous growth; environmental quality; status-seeking; public expenditure; Wagner's law.
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