Some calculations for TRISTAN

I took only few topics to investigate, some on which I had some personal interest, and others that I felt rather crucial for the design. In this document I report my calculations on these various subjects. Therefore this document represents my tangible contribution to TRISTAN design. I give in the following the list of the topics which are discussed in this document. 1. Increase of the vertical betatron emmitance by skew quadrupoles in the electron storage ring. 2. Bremsstrahlung. 3. Dipole correcting system for electron ring. 4. Wigglers at low energies 5. Steady state compensation of beam loading in the single beam mode in the electron storage ring. 6. Coupled bunch longitudinal instability for electron ring. 7. Ion production and trapping in the electron storage ring for TRISTAN. 8. Estimate of the longitudinal impedance for the TRISTAN electron storage ring. (author)