Hyperbolic lines and the stratospheric polar vortex

The necessary and sufficient conditions for Lagrangian hyperbolicity recently derived in the literature are reviewed in the light of older concepts of effective local rotation in strain coordinates. In particular, we introduce the simple interpretation of the necessary condition as a constraint on the local angular displacement in strain coordinates. These mathematically rigorous conditions are applied to the winter stratospheric circulation of the southern hemisphere, using analyzed wind data from the European Center for Medium-Range Weather Forecasts. Our results demonstrate that the sufficient condition is too strong and the necessary condition is too weak, so that both conditions fail to identify hyperbolic lines in the stratosphere. However a phenomenological, nonrigorous, criterion based on the necessary condition reveals the hyperbolic structure of the flow. Another (still nonrigorous) alternative is the finite-size Lyapunov exponent (FSLE) which is shown to produce good candidates for hyperbolic lines. In addition, we also tested the sufficient condition for Lagrangian ellipticity and found that it is too weak to detect elliptic coherent structures (ECS) in the stratosphere, of which the polar vortex is an obvious candidate. Yet, the FSLE method reveals a clear ECS-like barrier to mixing along the polar vortex edge. Further theoretical advancement is needed to explain the apparent success of nonrigorous methods, such as the FSLE approach, so as to achieve a sound kinematic understanding of chaotic mixing in the winter stratosphere and other geophysical flows. (c) 2002 American Institute of Physics.     

Cycles with a chord are graceful

In this paper, we prove that every cycle plus a chord is graceful, thus answering a conjecture of R. Bodendiek, H. Schumacher, and H. Wegner.     

Electronic quasiparticle renormalization on the spin wave energy scale

High-resolution photoemission data of the (110) iron surface reveal the existence of well-defined metallic surface resonances in good correspondence to band calculations. Close to the Fermi level, their dispersion and momentum broadening display anomalies characteristic of quasiparticle renormalization due to coupling to bosonic excitations. Its energy scale exceeds that of phonons by far, and is in striking coincidence with that of the spin wave spectrum in iron. The self-energy behavior thus gives spectroscopic evidence of a quasiparticle mass enhancement due to electron-magnon coupling.     

Platinum(II)-catalyzed 1,6-diene cycloisomerizations: turnover in the absence of beta-hydride elimination

Electrophilic pincer-ligated Pt(II)-dications are efficient catalysts for the cycloisomerization of 1,6-dienes, initiated by alkene activation. The tridentate ligands inhibit beta-hydride elimination and thus enable cationic mechanisms that turnover by Pt(II) extrusion. PPP ligands lead to cyclopropane products, while PNP ligands provide cyclohexene products; mechanistic issues are also discussed.     

MRP-controlled batch-manufacturing environment under uncertainty

The overall aim of this research is to model the effects of uncertainty on delivery performance in an MRP-controlled batch-manufacturing environment with multi-product and multi-level dependent demand. To this end, MRP planning and batch-manufacturing system control architectures were modelled using simulation to implement the MRP release logic. Simulation and experimental design were carried out based on a real case enterprise. ANOVA showed that four uncertainty factors—namely late delivery from suppliers, machine breakdowns, process batch size increments and customer design changes—have significant effects on delivery performance. This ANOVA further showed that uncertainties create knock-on and compound effects; the latter are difficult to predict in practice. Significant two-way and three-way interactions among some uncertainty factors were also found, making it more difficult to characterise the precise factor effects. It was found that the more uncertain the environment is, the later the deliveries are. It can be concluded that MRP-controlled batch-manufacturing enterprises should diagnose uncertainties that are significantly affecting delivery performance, and tackle these uncertainties most urgently to prevent diffusion of knock-on and compound effects and improve delivery performance. This conclusion was validated through the case enterprise, for which significant delivery improvement has been achieved.     

Synthesis of novel 2,6-disubstituted-3,4-dimethylidene tetrahydropyrans via Prins-type cyclization

Synthesis of novel substituted tetrahydropyrans with adjacent exo-methylene groups at the C3 and C4 positions via Prins-type cyclization has been described.     

Extension theorems for paraboloids in the finite field setting

In this paper we study the L ^p ? L ^r boundedness of the extension operators associated with paraboloids in ${{\mathbb F}_{q}^{d}}In this paper we study the L ^p − L ^r boundedness of the extension operators associated with paraboloids in \mathbb F_q^d{{\mathbb F}_{q}^{d}} , where \mathbbF_q{\mathbb{F}_{q}} is a finite field of q elements. In even dimensions d ≥ 4, we estimate the number of additive quadruples in the subset E of the paraboloids, that is the number of quadruples (x,y,z,w) ? E⁴{(x,y,z,w) \in E^4} with x + y = z+w. As a result, in higher even dimensions, we obtain the sharp range of exponents p for which the extension operator is bounded, independently of q, from L ^p to L ⁴ in the case when −1 is a square number in \mathbbF_q{\mathbb{F}_{q}} . Using the sharp L ^p −L ⁴ result, we improve upon the range of exponents r, for which the L ² − L ^r estimate holds, obtained by Mockenhaupt and Tao (Duke Math 121:35–74, 2004) in even dimensions d ≥ 4. In addition, assuming that −1 is not a square number in \mathbbF_q{\mathbb{F}_{q}}, we extend their work done in three dimension to specific odd dimensions d ≥ 7. The discrete Fourier analytic machinery and Gauss sum estimates make an important role in the proof.     

On the factor-thickness of regular graphs

For eachr-regular graphG, define a binary sequence(G) = ( ₁, ₂,..., _r-1) by _k = 0 ifG has ak-factor, and _k = 1 otherwise. A binary sequence = ( _i |i = 1, 2,...,r – 1) is said to be realizable if there exists anr-regular graphG such that(G) = . In this paper we characterize all binary sequences which are realizable.