Positronium in a liquid phase: formation, bubble state and chemical reactions

This chapter reviews the following items: 1. Energy deposition and track structure of fast positrons: ionization slowing down, number of ion-electron pairs, typical sizes, thermalization, electrostatic interaction between e+ and its blob, effect of local heating; 2. Positronium formation in condensed media: the Ore model, quasifree Ps state, intratrack mechanism of Ps formation; 3. Fast intratrack diffusion-controlled reactions: Ps oxidation and ortho-para conversion by radiolytic products, reaction rate constants, interpretation of the PAL spectra in water at different temperatures; 4. Ps bubble models. "Non-point" positronium: wave function, energy contributions, relationship between the pick-off annihilation rate and the bubble radius

Semiclassical treatment of logarithmic perturbation theory

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and exited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues of the harmonic oscillator perturbed by $\lambda x^{6}$ are considered.Comment: 6 pages, LATEX 2.09 using IOP style

Resilience of Volatility

The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is suggested of the emergence of significant serial autocorrelations in volatility and squared returns. It is shown that when non-stationarity is eliminated, the autocorrelations substantially reduce and become statistically insignificant. The causes of non-Gaussian nature of the probability of returns distribution are considered. For both stock and currency markets data samples, it is shown that removing the non-stationary component substantially reduces the kurtosis of distribution, bringing it closer to the Gaussian one. A statistical criterion is proposed for controlling the degree of smoothing of the empirical values of volatility. The hypothesis of smooth, non-stochastic nature of volatility is put forward, and possible causes of volatility shifts are discussed.Comment: 30 pages with 33 figures, uses wrapfig.st

Relationship between sectional curvature and null spaces of Lichnerowicz-type Laplacians and their smallest eigenvalues

In the paper, we prove that the curvature operator of the second kind of Riemannian manifolds is positive (respectively, negative) if and only if its sectional curvature is also positive (respectively, negative). In addition, we prove several vanishing theorems on null spaces of the Lichnerowicz, Sampson and Hodge-de Rham Laplacians and we find estimates of their lowest eigenvalues on closed Riemannian manifolds of sign-definite sectional curvature