7,380 research outputs found
Sovereign Wealth Funds in the Next Decade
A prolonged and multispeed recovery period, its associated policy response, and the new global financial landscape might have important bearing on the size and allocation of sovereign wealth funds (SWFs) assets. SWFs could become a driving force in South-South flows, boosting global wealth by helping recycle large savings in surplus countries toward more productive investments. Whereas they indeed represent a new opportunity for developing countries, they also carry challenges for both home and host countries.Sovereign wealth funds, SWF, recovery, economic recovery, financial crisis, investments, developing countries, South-South, savings, surplus
Subnormality for arbitrary powers of 2-variable weighted shifts whose restrictions to a large invariant subspace are tensor products
The Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and
sufficient conditions for a pair of subnormal operators on Hilbert space to
admit commuting normal extensions. \ We study LPCS within the class of
commuting 2-variable weighted shifts with
subnormal components and , acting on the Hilbert space with canonical orthonormal basis
. \ The \textit{core} of a commuting
2-variable weighted shift , , is the restriction of
to the invariant subspace generated by all vectors
with ; we say that is of \textit{tensor form}
if it is unitarily equivalent to a shift of the form , where and are subnormal unilateral
weighted shifts. \ Given a 2-variable weighted shift whose core is
of tensor form, we prove that LPCS is solvable for if and only if
LPCS is solvable for any power (). \Comment: article in pres
When is hyponormality for 2-variable weighted shifts invariant under powers?
For 2-variable weighted shifts W_{(\alpha,\beta)}(T_1, T_2) we study the
invariance of (joint) k- hyponormality under the action (h,\ell) ->
W_{(\alpha,\beta)}^{(h,\ell)}(T_1, T_2):=(T_1^k,T_2^{\ell}) (h,\ell >=1). We
show that for every k >= 1 there exists W_{(\alpha,\beta)}(T_1, T_2) such that
W_{(\alpha,\beta)}^{(h,\ell)}(T_1, T_2) is k-hyponormal (all h>=2,\ell>=1) but
W_{(\alpha,\beta)}(T_1, T_2) is not k-hyponormal. On the positive side, for a
class of 2-variable weighted shifts with tensor core we find a computable
necessary condition for invariance. Next, we exhibit a large nontrivial class
for which hyponormality is indeed invariant under all powers; moreover, for
this class 2-hyponormality automatically implies subnormality. Our results
partially depend on new formulas for the determinant of generalized Hilbert
matrices and on criteria for their positive semi-definiteness
Threefold Flops via Matrix Factorization
The explicit McKay correspondence, as formulated by Gonzalez-Sprinberg and
Verdier, associates to each exceptional divisor in the minimal resolution of a
rational double point a matrix factorization of the equation of the rational
double point. We study deformations of these matrix factorizations, and show
that they exist over an appropriate "partially resolved" deformation space for
rational double points of types A and D. As a consequence, all simple flops of
lengths 1 and 2 can be described in terms of blowups defined from matrix
factorizations. We also formulate conjectures which would extend these results
to rational double points of type E and simple flops of length greater than 2.Comment: v2: minor change
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