Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds

The precise relation between Kodaira-Spencer path integral and a particular wave function in seven dimensional quadratic field theory is established. The special properties of three-forms in 6d, as well as Hitchin's action functional, play an important role. The latter defines a quantum field theory similar to Polyakov's formulation of 2d gravity; the curious analogy with world-sheet action of bosonic string is also pointed out.Comment: 31 page

Non-autonomous Hamiltonian systems related to highest Hitchin integrals

We describe non-autonomous Hamiltonian systems coming from the Hitchin integrable systems. The Hitchin integrals of motion depend on the W-structures of the basic curve. The parameters of the W-structures play the role of times. In particular, the quadratic integrals dependent on the complex structure (W_2-structure) of the basic curve and times are coordinate on the Teichmuller space. The corresponding flows are the monodromy preserving equations such as the Schlesinger equations, the Painleve VI equation and their generalizations. The equations corresponding to the highest integrals are monodromy preserving conditions with respect to changing of the W_k-structures (k>2). They are derived by the symplectic reduction from the gauge field theory on the basic curve interacting with W_k-gravity. As by product we obtain the classical Ward identities in this theory.Comment: 21 pages,Latex, Contribution in the Proceedings "International Seminar on Integrable systems". In memoriam Mikail V. Saveliev. Bonn, February, 199

Quantum matter wave dynamics with moving mirrors

When a stationary reflecting wall acting as a perfect mirror for an atomic beam with well defined incident velocity is suddenly removed, the density profile develops during the time evolution an oscillatory pattern known as diffraction in time. The interference fringes are suppressed or their visibility is diminished by several effects such as averaging over a distribution of incident velocities, apodization of the aperture function, atom-atom interactions, imperfect reflection or environmental noise. However, when the mirror moves with finite velocity along the direction of propagation of the beam, the visibility of the fringes is enhanced. For mirror velocities below beam velocity, as used for slowing down the beam, the matter wave splits into three regions separated by space-time points with classical analogues. For mirror velocities above beam velocity a visibility enhancement occurs without a classical counterpart. When the velocity of the beam approaches that of the mirror the density oscillations rise by a factor 1.8 over the stationary value.Comment: 5.2 pages, 6 figure

Rational symplectic coordinates on the space of Fuchs equations m×mm \times m-case

A method of constructing of Darboux coordinates on a space that is a symplectic reduction with respect to a diagonal action of GL(m}) on a Cartesian product of $N$ orbits of coadjoint representation of $GL(m)$ is presented. The method gives an explicit symplectic birational isomorphism between the reduced space on the one hand and a Cartesian product of $N-3$ coadjoint orbits of dimension $m(m-1)$ on an orbit of dimension $(m-1)(m-2)$ on the other hand. In a generic case of the diagonalizable matrices it gives just the isomorphism that is birational and symplectic between some open, in a Zariski topology, domain of the reduced space and the Cartesian product of the orbits in question. The method is based on a Gauss decomposition of a matrix on a product of upper-triangular, lower-triangular and diagonal matrices. It works uniformly for the orbits formed by diagonalizable or not-diagonalizable matrices. It is elaborated for the orbits of maximal dimension that is $m(m-1)$.Comment: 11 page

Proton structure corrections to electronic and muonic hydrogen hyperfine splitting

We present a precise determination of the polarizability and other proton structure dependent contributions to the hydrogen hyperfine splitting, based heavily on the most recent published data on proton spin dependent structure functions from the EG1 experiment at the Jefferson Laboratory. As a result, the total calculated hyperfine splitting now has a standard deviation slightly under 1 part-per-million, and is about 1 standard deviation away from the measured value. We also present results for muonic hydrogen hyperfine splitting, taking care to ensure the compatibility of the recoil and polarizability terms.Comment: 9 pages, 1 figur

Cartridge toolholders and boring heads for high-precision holes treatment

The analysis of cartridge tool holders and boring heads constructions was done, the constructions of micrometer adjustment of blades were considered, models and results of stress, displacement and safety factor for split bushing are shown

Design Features of Instruments in Automated Production Facilities

The article deals with designing cutting tools in automated production facilities and with their main features – interchangeability, versatility, high accuracy