On AGT conjecture

In these notes we consider relation between conformal blocks and the Nekrasov partition function of certain $\mathcal{N}=2$ SYM theories proposed recently by Alday, Gaiotto and Tachikawa. We concentrate on $\mathcal{N}=2^{*}$ theory, which is the simplest example of AGT relation.Comment: References adde

Multipoint correlation functions in Liouville field theory and minimal Liouville gravity

We study n+3-point correlation functions of exponential fields in Liouville field theory with n degenerate and 3 arbitrary fields. An analytical expression for these correlation functions is derived in terms of Coulomb integrals. The application of these results to the minimal Liouville gravity is considered.Comment: Contribution to the proceedings of the International Workshop on Classical and Quantum Integrable Systems, Dubna, Russia, January 22-25, 2007, 18 page

Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations

We study the conformal vertex algebras which naturally arise in relation to the Nakajima-Yoshioka blow-up equations.Comment: 23 pages v2. 24 pages, references added, proofs in section 3 are expanded, many typos correcte

Isochronicity Correction in the CR Storage Ring

A challenge for nuclear physics is to measure masses of exotic nuclei up to the limits of nuclear existence which are characterized by low production cross sections and short half-lives. The large acceptance Collector Ring (CR) at FAIR tuned in the isochronous ion-optical mode offers unique possibilities for measuring short-lived and very exotic nuclides. However, in a ring designed for maximal acceptance, many factors limit the resolution. One point is a limit in time resolution inversely proportional to the transverse emittance. But most of the time aberrations can be corrected and others become small for large number of turns. We show the relations of the time correction to the corresponding transverse focusing and that the main correction for large emittance corresponds directly to the chromaticity correction for transverse focusing of the beam. With the help of Monte-Carlo simulations for the full acceptance we demonstrate how to correct the revolution times so that in principle resolutions of dm/m=1E-6 can be achieved. In these calculations the influence of magnet inhomogeneities and extended fringe fields are considered and a calibration scheme also for ions with different mass-to-charge ratio is presented.Comment: 6 figures, recised version May 201

Hyperfine-induced effects on the linear polarization of the Kα1\alpha_1 emission from helium-like ions

The linear polarization of the characteristic photon emission from few-electron ions is studied for its sensitivity with regard to the nuclear spin and magnetic moment of the ions. Special attention is paid, in particular, to the K$\alpha_1$ (1s 2p_{3/2} ^{1,3}P_{1,2} \to 1s^2 ^1S_0) decay of selected helium-like ions following the radiative electron capture into initially hydrogen-like species. Based on the density matrix theory, a unified description is developed that includes both, the many-electron and hyperfine interactions as well as the multipole-mixing effects arising from the expansion of the radiation field. It is shown that the polarization of the K$\alpha_1$ line can be significantly affected by the mutipole mixing between the leading $M2$ and hyperfine-induced $E1$ components of 1s2p ^3P_2, F_i \to 1s^2 ^1S_0, F_f transitions. This $E1$-$M2$ mixing strongly depends on the nuclear properties of the considered isotopes and can be addressed experimentally at existing heavy-ion storage rings

Sensor Explosive Concentrations of Hydrogen

The article describes a resistive sensor explosive concentrations of hydrogen with a response time of about 0.1 s is completely selective for hydrogen