Jordan curves and funnel sections

We study the case when solution of an ODE at a given initial condition fail to be unique and investigate what are the possible time-1 sections of the `solution funnel'. Along the way we give construction of a natural complete metric on the space of Jordan curves and prove that the generic Jordan curve is nowhere pierceable by arcs of finite length.Comment: 22 pages, 16 figure

Lee-Yang Property and Gaussian multiplicative chaos

The Lee-Yang property of certain moment generating functions having only pure imaginary zeros is valid for Ising type models with one-component spins and XY models with two-component spins. Villain models and complex Gaussian multiplicative chaos are two-component systems analogous to XY models and related to Gaussian free fields. Although the Lee-Yang property is known to be valid generally in the first case, we show that is not so in the second. Our proof is based on two theorems of general interest relating the Lee-Yang property to distribution tail behavior.Comment: We changed the title to emphasize Gaussian multiplicative chaos. Theorem 11, giving criteria for when some zeros are not purely imaginary, has been considerably strengthened. This yields a correspondingly improved result for continuum complex Gaussian multiplicative chaos in Proposition 1

Symmetry of Hydrogen Bonds in Two Enols in Solution.

The enols of 4-cyano-2,2,6,6-tetramethyl-3,5-heptanedione and of nitromalonamide were prepared as statistical mixtures of 18O n ( n = 0, 1, 2) isotopologues. The symmetries of their hydrogen bonds were probed by isotopic perturbation of their 13CO NMR signals. The former mixture shows a total of four signals, due to both intrinsic and perturbation isotope shifts. Therefore, that enol is a mixture of tautomers with an asymmetric hydrogen bond. In contrast, the mixture of isotopologues of nitromalonamide enol shows only two signals, due to an intrinsic isotope shift. Therefore, this is the first case, to be compared with the FHF- anion, of a neutral species with a single symmetric structure in solution and with a centered hydrogen

An XPS Study of the Radiation-induced Effect on the Thermal Degradation and Charring of Butadiene and its Copolymers

A pseudo-in-situ XPS approach shows that cross-linking induced by irradiation may lead to char formation even though it shows only a small or no effect on the onset temperature of degradation

Can long-horizon forecasts beat the random walk under the Engel-West explanation?

Engel and West (EW, 2005) argue that as the discount factor gets closer to one, present-value asset pricing models place greater weight on future fundamentals. Consequently, current fundamentals have very weak forecasting power and exchange rates appear to follow approximately a random walk. We connect the Engel-West explanation to the studies of exchange rates with long-horizon regressions. We find that under EW's assumption that fundamentals are I(1) and observable to the econometrician, long-horizon regressions generally do not have significant forecasting power. However, when EW's assumptions are violated in a particular way, our analytical results show that there can be substantial power improvements for long-horizon regressions, even if the power of the corresponding short-horizon regression is low. We simulate population R squared for long-horizon regressions in the latter setting, using Monetary and Taylor Rule models of exchange rates calibrated to the data. Simulations show that long-horizon regression can have substantial forecasting power for exchange rates.Foreign exchange rates ; Financial markets ; Asset pricing ; Forecasting ; Random walks (Mathematics) ; Regression analysis