6,256 research outputs found
Optimal Diversity in Investments with Recombinant Innovation
The notion of dynamic, endogenous diversity and its role in theories of investment and technological innovation is addressed. We develop a formal model of an innovation arising from the combination of two existing modules with the objective to optimize the net benefits of diversity. The model takes into account increasing returns to scale and the effect of different dimensions of diversity on the probability of emergence of a third option. We obtain analytical solutions describing the dynamic behaviour of the values of the options. Next diversity is optimized by trading off the benefits of recombinant innovation and returns to scale. We derive conditions for optimal diversity under different regimes of returns to scale. Threshold values of returns to scale and recombination probability define regions where either specialization or diversity is the best choice. In the time domain, when the investment time horizon is beyond a threshold value, a diversified investment becomes the best choice. This threshold will be larger the higher the returns to scale.
Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities
Let X be a surface with an isolated singularity at the origin, given by the
equation Q(x,y,z)=0, where Q is a weighted-homogeneous polynomial. In
particular, this includes the Kleinian surfaces X = C^2/G for G < SL(2,C)
finite. Let Y be the n-th symmetric power of X. We compute the zeroth Poisson
homology of Y, as a graded vector space with respect to the weight grading. In
the Kleinian case, this confirms a conjecture of Alev, that the zeroth Poisson
homology of the n-th symmetric power of C^2/G is isomorphic to the zeroth
Hochschild homology of the n-th symmetric power of the algebra of G-invariant
differential operators on C. That is, the Brylinski spectral sequence
degenerates in this case. In the elliptic case, this yields the zeroth
Hochschild homology of symmetric powers of the elliptic algebras with three
generators modulo their center, for the parameter equal to all but countably
many points of the elliptic curve.Comment: 17 page
Rotating solenoidal perfect fluids of Petrov type D
We prove that aligned Petrov type D perfect fluids for which the vorticity
vector is not orthogonal to the plane of repeated principal null directions and
for which the magnetic part of the Weyl tensor with respect to the fluid
velocity has vanishing divergence, are necessarily purely electric or locally
rotationally symmetric. The LRS metrics are presented explicitly.Comment: 6 pages, no figure
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