Investigation of flat spectrum radio sources by the interplanetary scintillation method at 111 MHz

Abstract. Interplanetary scintillation observations of 48 of the 55 Augusto et al. (1998) flat spectrum radio sources were carried out at 111 MHz using the interplanetary scintillation method on the Large Phased Array (LPA) in Russia. Due to the large size of the LPA beam (1◦ × 0.5◦) a careful inspection of all possible confusion sources was made using extant large radio surveys: 37 of the 48 sources are not confused. We were able to estimate the scintillating flux densities of 13 sources, getting upper limits for the remaining 35. Gathering more or improving extant VLBI data on these sources might significantly improve our results. This proof-of-concept project tells us that compact (<1 ) flat spectrum radio sources show strong enough scintillations at 111 MHz to establish/constrain their spectra (low-frequency end). Key words. galaxies: general – galaxies: active – galaxies: quasars: general

On invariant Rings of Sylow subgroups of finite classical groups

In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups.