Optimal control of the heave motion of marine cable subsea-unit systems

One of the key problems associated with subsea operations involving tethered subsea units is the motions of support vessels on the ocean surface which can be transmitted to the subsea unit through the cable and increase the tension. In this paper, a theoretical approach for heave compensation is developed. After proper modelling of each element of the system, which includes the cable/subsea-unit, the onboard winch, control theory is applied to design an optimal control law. Numerical simulations are carried out, and it is found that the proposed active control scheme appears to be a promising solution to the problem of heave compensation

Concerning LpL^p resolvent estimates for simply connected manifolds of constant curvature

We prove families of uniform $(L^r,L^s)$ resolvent estimates for simply connected manifolds of constant curvature (negative or positive) that imply the earlier ones for Euclidean space of Kenig, Ruiz and the second author \cite{KRS}. In the case of the sphere we take advantage of the fact that the half-wave group of the natural shifted Laplacian is periodic. In the case of hyperbolic space, the key ingredient is a natural variant of the Stein-Tomas restriction theorem.Comment: 25 pages, 2 figure

Economic Analysis of Sequestering Carbon in Green Ash Forests in the Lower Mississippi River Valley

Since the U.S. is the largest emitter of carbon dioxide (CO2), it has become crucial to develop options that are both cost effective and supportive of sustainable development to reduce atmospheric CO2. Electric utility companies have the options of reducing their use of fossil fuels, switching to alternative energy sources, increasing efficiency, or offsetting carbon emissions. This study determined the cost and profitability of sequestering carbon in green ash plantations, and the number of tons of carbon that can be sequestered. The profitability of green ash is $2,342 and$3,645 per acre on site indices (measurement of soil quality) 65 and 105 land, respectively, calculated with a 2.5% alternative rate of return (ARR). These figures shift to –$248 and –$240 calculated with a 15.0% ARR. If landowners who have an ARR of 2.5% can sell carbon credits for $10 per ton of carbon, profits will increase by$107 per acre on poor sites and $242 on good sites. Over one rotation (cutting cycle), 38.56 net tons of carbon can be sequestered on an acre of poor quality land and 51.35 tons on good quality land. The cost of sequestering carbon, without including revenues from timber production and carbon credits, ranges from a high of$15.20 per ton on poor sites to $14.41 on good sites, calculated with a 2.5$8.51 per ton on poor sites to $7.63 on good sites, calculated with a 15.0% ARR. The cost of storing carbon can be reduced significantly if the trees can be sold for wood products

The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics

We consider the class of Levi nondegenerate hypersurfaces $M$ in \bC^{n+1} that admit a local (CR transversal) embedding, near a point $p\in M$, into a standard nondegenerate hyperquadric in $\Bbb C^{N+1}$ with codimension $k:=N-n$ small compared to the CR dimension $n$ of $M$. We show that, for hypersurfaces in this class, there is a normal form (which is closely related to the embedding) such that any local equivalence between two hypersurfaces in normal form must be an automorphism of the associated tangent hyperquadric. We also show that if the signature of $M$ and that of the standard hyperquadric in \bC^{N+1} are the same, then the embedding is rigid in the sense that any other embedding must be the original embedding composed with an automorphism of the quadric

Rotating Stellar Models Can Account for the Extended Main Sequence Turnoffs in Intermediate Age Clusters

We show that the extended main sequence turnoffs seen in intermediate age Large Magellanic Cloud (LMC) clusters, often attributed to age spreads of several hundred Myr, may be easily accounted for by variable stellar rotation in a coeval population. We compute synthetic photometry for grids of rotating stellar evolution models and interpolate them to produce isochrones at a variety of rotation rates and orientations. An extended main sequence turnoff naturally appears in color-magnitude diagrams at ages just under 1 Gyr, peaks in extent between ~1 and 1.5 Gyr, and gradually disappears by around 2 Gyr in age. We then fit our interpolated isochrones by eye to four LMC clusters with very extended main sequence turnoffs: NGC 1783, 1806, 1846, and 1987. In each case, stellar populations with a single age and metallicity can comfortably account for the observed extent of the turnoff region. The new stellar models predict almost no correlation of turnoff color with rotational vsini: the red edge of the turnoff is populated by a combination of slow rotators and edge-on rapid rotators.Comment: 7 pages, 4 figures, 1 table, ApJ accepted. Conclusions unchange

Tax fraud by firms and optimal auditing

Abstract Tax fraud is an issue of increasing importance in China. One particularly signi…cant fraud involves excessive claims for the rebate of VAT on exported goods. This fraud has two interesting features. First, it requires the collusion of an intermediary to supply the false documentation that supports a rebate application. Second, the punishment schedule is convex -with capital punishment used in major fraud cases. These features ensure that the payo¤ function of a …rm engaging in fraud is strictly concave in the level of fraud. This gives a well-de…ned optimization without the need to appeal to risk aversion. We show that the existence of fraud does not a¤ect the real output decision of the …rm nor the tax policy of the government. Audit resources can be used to detect …rms engaged in fraud as well as the intermediaries who supply false documents. Under reasonable assumptions it is shown that resources should be focused on detecting …rms and not intermediaries. Finally, if the government must take action on fraud a convex punishment scheme is shown to be optimal