Period integrals of CY and general type complete intersections

We develop a global Poincaré residue formula to study period integrals of families of complex manifolds. For any compact complex manifold X equipped with a linear system V ^? of generically smooth CY hypersurfaces, the formula expresses period integrals in terms of a canonical global meromorphic top form on X. Two important ingredients of this construction are the notion of a CY principal bundle, and a classification of such rank one bundles. We also generalize the construction to CY and general type complete intersections. When X is an algebraic manifold having a sufficiently large automorphism group G and V ^? is a linear representation of G, we construct a holonomic D-module that governs the period integrals. The construction is based in part on the theory of tautological systems we have developed in the paper Lian, Song and Yau (arXiv:1105.2984v1, 2011). The approach allows us to explicitly describe a Picard-Fuchs type system for complete intersection varieties of general types, as well as CY, in any Fano variety, and in a homogeneous space in particular. In addition, the approach provides a new perspective of old examples such as CY complete intersections in a toric variety or partial flag variety.     

Lower Bounds on the Blow-Up Rate of the Axisymmetric Navier–Stokes Equations II

Consider axisymmetric strong solutions of the incompressible Navier–Stokes equations in ?³ with non-trivial swirl. Let z denote the axis of symmetry and r measure the distance to the z-axis. Suppose the solution satisfies, for some 0 ≤ ε ≤ 1, |v (x, t)| ≤ C _? r ^?1+ε |t|^?ε/2 for ? T ₀ ≤ t < 0 and 0 < C _? < ∞ allowed to be large. We prove that v is regular at time zero.     

Determination of cyanobacterial cyclic peptide hepatotoxins in drinking water using CE

Four cyanobacteria hepatotoxins microcystin LR, microcystin RR, microcystin YR, and nodularin were simultaneously determined in drinking water using CZE and MEKC coupled with UV detection. The toxins were satisfactorily separated in both CZE and MEKC modes. Detection limits were in the range of 0.82–4.81 μg/mL, with R² values of 0.994–0.999. The linearity range tested for the standards was 5–100 μg/mL and RSD percentages were in the range of 1.0–2.5% for retention time and 3.0–10.2% for peak area. When a known amount of standard was spiked into a known volume of water and extracted, recoveries were 90.3% (RR), 101.5% (nodularin), 90.6% (YR), and 88.2% (LR). The use of SPE enabled cleanup and pre‐concentration of a real sample to achieve a 100‐fold concentration factor. Detection limits after SPE of the real sample spiked with microcystins were 0.090 μg/L (RR), 0.076 μg/L (YR), and 0.110 μg/L (LR), with RSD percentage values of 9.9–11.7% for peak area and 2.2–3.3% for retention time. The technique developed provides an alternative method for determining microcystins at levels of concentration that will be able to meet WHO drinking water guidelines for microcystins.     

Classification of gradient space of dimension 8 by a reducible <Emphasis Type="Italic">s</Emphasis>ℓ(2, C) action

This paper deals with a reducible sℓ(2,C) action on the formal power series ring. The purpose of this paper is to confirm a special case of the Yau conjecture: Suppose that sℓ(2,C) acts on the formal power series ring via (1.1). Then I(f) = (ℓ _i1) ⊕ (ℓ _i2) ⊕... ⊕ (ℓ _is ) modulo some one dimensional sℓ(2,C) representations where (ℓ _i ) is an irreducible sℓ(2,C) representation of ℓ _i dimension and {ℓ _i1 ℓ _i2,...,ℓ _is } ⊆ {ℓ ₁ , ℓ ₂...,ℓ _r }. Unlike classical invariant theory which deals only with irreducible action and 1-dimensional representations, we treat the reducible action and higher dimensional representations successively.     

Nested partitions for the large-scale extended job shop scheduling problem

This paper addresses the large-scale extended job shop scheduling problem while considering the bill of material and the working shifts constraints. We propose two approaches for the problem. One is based on dispatching rules (DR), and the other is an application of the Nested Partitions (NP) Framework. A sampling approach for the exact feasible subregion is developed to complete the NP method. Furthermore, to efficiently search each subregion, a weighted sampling approach is also presented. Computational experiments show that the NP method with weighted sampling can find good solutions for most large-scale extended job shop scheduling problems.     

The existence of a black hole due to condensation of matter

When enough matter is condensed in a small region, gravitational effects will be strong enough to cause collapse and a black hole will be formed. We formulate and prove here such a statement in the language of general relativity. (This is Theorem 2 of this paper.)     

Positivity of quasilocal mass

Motivated by the important work of Brown and York on quasilocal energy, we propose definitions of quasilocal energy and momentum surface energy of a spacelike 2-surface with a positive intrinsic curvature in a spacetime. We show that the quasilocal energy of the boundary of a compact spacelike hypersurface which satisfies the local energy condition is strictly positive unless the spacetime is flat along the spacelike hypersurface.     

Time-resolved resonance Raman and density functional study of an azirine intermediate in the 2-fluorenylnitrene ring-expansion reaction to form a dehydroazepine product

We report time-resolved resonance Raman spectra for the azirine intermediate produced in the 2-fluorenylnitrene ring-expansion reaction to form a dehydroazepine product. The Raman bands obtained with a 252.7 nm probe wavelength and 500 ns delay time exhibit reasonable agreement with predicted vibrational frequencies from density functional calculations for two isomers of azirine intermediates that may be formed from a 2-fluorenylnitrene precursor. The Raman bands observed for delay times of 15 ns and 10 micros were consistent with predicted vibrational frequencies from density functional calculations for the 2-fluorenylnitrene and dehydroazepine product species as well as previously reported 416 nm time-resolved Raman spectra obtained on the ns and micros time scales. Our results demonstrate that the 2-fluorenylnitrene ring-expansion reaction to produce dehydroazepine products proceeds via relatively long-lived 2-fluorenylnitrene and azirine intermediates. Substitution of a phenyl ring para to the nitrene group of phenylnitrene appears to lead to significant changes in the ring-expansion reaction so that longer lived arylnitrene and azirine intermediates can be observed. This should enable the chemical reactivity of azirine intermediates formed from arylnitrenes to be examined more readily.