A generating functional approach to the Hubbard model

The method of generating functional is generalized to the case of strongly correlated systems, and applied to the Hubbard model. For the electronic Green's function constructed for Hubbard operators, an equation using variational derivatives with respect to the fluctuating fields has been derived and its multiplicative form has been determined. Corrections for the electronic self-energy are calculated up to the second order with respect to the parameter W/U (W width of the band), and a mean field type approximation was formulated, including both charge and spin static fluctuations. The equations for the Bose-like Green's functions have been derived, describing the collective modes: the magnons and doublons. The properties of the poles of the doublon Green's functions depend on electronic filling. The investigation of the special case n=1 demonstrates that the doublon Green's function has a soft mode at the wave vector Q=(pi,pi,...), indicating possible instability of the uniform paramagnetic phase relatively to the two sublattices charge ordering. However this instability should compete with an instability to antiferromagnetic ordering.Comment: 31 pages, 7 figures, to be published in Eur. Phys. J.

On Possible Measurement of Gravitational Interaction Parameters on Board a Satellite

The recently suggested SEE (Satellite Energy Exchange) method of measuring the gravitational constant $G$, possible equivalence principle violation (measured by the E\"{o}tv\"{o}s parameter $\eta$) and the hypothetic 5th force parameters $\alpha$ and $\lambda$ on board a drag-free Earth's satellite is discussed and further developed. Various particle trajectories near a heavy ball are numerically simulated. Some basic sources of error are analysed. The $G$ measurement procedure is modelled by noise insertion to a ``true'' trajectory. It is concluded that the present knowledge of $G, \alpha$ (for $\lambda \geq 1$ m) and $\eta$ can be improved by at least two orders of magnitude.Comment: (only two misprints on title page) 7 page

On birational involutions of P3P^3

Let $X$ be a rationally connected three-dimensional algebraic variety and let $\tau$ be an element of order two in the group of its birational selfmaps. Suppose that there exists a non-uniruled divisorial component of the $\tau$-fixed point locus. Using the equivariant minimal model program we give a rough classification of such elements.Comment: 24 pages, late

Preimaginal Stages of the Emerald Ash Borer, Agrilus planipennis Fairmaire (Coleoptera: Buprestidae): An Invasive Pest on Ash Trees (Fraxinus)

This study provides the most detailed description of the immature stages of Agrilus planipennis Fairmaire to date and illustrates suites of larval characters useful in distinguishing among Agrilus Curtis species and instars. Immature stages of eight species of Agrilus were examined and imaged using light and scanning electron microscopy. For A. planipennis all preimaginal stages (egg, instars I-IV, prepupa and pupa) were described. A combination of 14 character states were identified that serve to identify larvae of A. planipennis. Our results support the segregation of Agrilus larvae into two informal assemblages based on characters of the mouthparts, prothorax, and abdomen: the A. viridis and A. ater assemblages, with A. planipennis being more similar to the former. Additional evidence is provided in favor of excluding A. planipennis from the subgenus Uragrilus