The NASA high-speed turboprop program

Technology readiness for Mach 0.7 to 0.8 turboprop powered aircraft with the potential for fuel savings and DOC reductions of up to 30 and 15 percent respectively relative to current in-service aircraft is addressed. The areas of propeller aeroacoustics, propeller structures, turboprop installed performance, aircraft cabin environment, and turboprop engine and aircraft studies are emphasized. Large scale propeller characteristics and high speed propeller flight research tests using a modified testbed aircraft are also considered

Birational cobordism invariance of uniruled symplectic manifolds

A symplectic manifold $(M,\omega)$ is called {\em (symplectically) uniruled} if there is a nonzero genus zero GW invariant involving a point constraint. We prove that symplectic uniruledness is invariant under symplectic blow-up and blow-down. This theorem follows from a general Relative/Absolute correspondence for a symplectic manifold together with a symplectic submanifold. A direct consequence is that symplectic uniruledness is a symplectic birational invariant. Here we use Guillemin and Sternberg's notion of cobordism as the symplectic analogue of the birational equivalence.Comment: To appear in Invent. Mat

Log Fano varieties over function fields of curves

Consider a smooth log Fano variety over the function field of a curve. Suppose that the boundary has positive normal bundle. Choose an integral model over the curve. Then integral points are Zariski dense, after removing an explicit finite set of points on the base curve.Comment: 18 page

Difference in Brain Densities Between Chronic Alcoholic and Normal Control Patients.

The densities of the brains of 11 chronic alcoholics were compared with those of 11 age-matched normal control subjects. Densities were determined from the density numbers generated by computerized tomography at three levels of the brain-the highest level of the lateral ventricles and the next two higher levels-with adjustments made to control for possible artifacts in the data. The advantage of the dominant hemisphere over the nondominant hemisphere was lessened in alcoholic

Holomorphic anomaly equations and the Igusa cusp form conjecture

Let $S$ be a K3 surface and let $E$ be an elliptic curve. We solve the reduced Gromov-Witten theory of the Calabi-Yau threefold $S \times E$ for all curve classes which are primitive in the K3 factor. In particular, we deduce the Igusa cusp form conjecture. The proof relies on new results in the Gromov-Witten theory of elliptic curves and K3 surfaces. We show the generating series of Gromov-Witten classes of an elliptic curve are cycle-valued quasimodular forms and satisfy a holomorphic anomaly equation. The quasimodularity generalizes a result by Okounkov and Pandharipande, and the holomorphic anomaly equation proves a conjecture of Milanov, Ruan and Shen. We further conjecture quasimodularity and holomorphic anomaly equations for the cycle-valued Gromov-Witten theory of every elliptic fibration with section. The conjecture generalizes the holomorphic anomaly equations for ellliptic Calabi-Yau threefolds predicted by Bershadsky, Cecotti, Ooguri, and Vafa. We show a modified conjecture holds numerically for the reduced Gromov-Witten theory of K3 surfaces in primitive classes.Comment: 68 page

Anomalous layering at the liquid Sn surface

X-ray reflectivity measurements on the free surface of liquid Sn are presented. They exhibit the high-angle peak, indicative of surface-induced layering, also found for other pure liquid metals (Hg, Ga and In). However, a low-angle peak, not hitherto observed for any pure liquid metal, is also found, indicating the presence of a high-density surface layer. Fluorescence and resonant reflectivity measurements rule out the assignment of this layer to surface-segregation of impurities. The reflectivity is modelled well by a 10% contraction of the spacing between the first and second atomic surface layers, relative to that of subsequent layers. Possible reasons for this are discussed.Comment: 8 pages, 9 figures; to be submitted to Phys. Rev. B; updated references, expanded discussio

On the Crepant Resolution Conjecture in the Local Case

In this paper we analyze four examples of birational transformations between local Calabi-Yau 3-folds: two crepant resolutions, a crepant partial resolution, and a flop. We study the effect of these transformations on genus-zero Gromov-Witten invariants, proving the Coates-Corti-Iritani-Tseng/Ruan form of the Crepant Resolution Conjecture in each case. Our results suggest that this form of the Crepant Resolution Conjecture may also hold for more general crepant birational transformations. They also suggest that Ruan's original Crepant Resolution Conjecture should be modified, by including appropriate "quantum corrections", and that there is no straightforward generalization of either Ruan's original Conjecture or the Cohomological Crepant Resolution Conjecture to the case of crepant partial resolutions. Our methods are based on mirror symmetry for toric orbifolds.Comment: 27 pages. This is a substantially revised and shortened version of my preprint "Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples"; all results contained here are also proved there. To appear in Communications in Mathematical Physic

Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

We present a proof of the mirror conjecture of Aganagic-Vafa [arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in the total space of the canonical line bundle of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]), and (iii) an outer brane at zero framing in the total space of the canonical line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).Comment: 39 pages, 11 figure

Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms

Given any smooth toric surface S, we prove a SYM-HILB correspondence which relates the 3-point, degree zero, extended Gromov-Witten invariants of the n-fold symmetric product stack [Sym^n(S)] of S to the 3-point extremal Gromov-Witten invariants of the Hilbert scheme Hilb^n(S) of n points on S. As we do not specialize the values of the quantum parameters involved, this result proves a strengthening of Ruan's Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphism from Hilb^n(S) to Sym^n(S) and yields a method of reconstructing the cup product for Hilb^n(S) from the orbifold invariants of [Sym^n(S)].Comment: Revised versio