In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part, according to variational approach we obtain a representation for orbital particle motion in storage rings as a multiresolution (multiscales) expansion in the base of welllocalized in phase space wavelet basis. By mea...

It has been shown that high performance cavity BPM's are capable of accurate beam trajectory angle and beam ‘tilt’, (x-z or y-z correlation) measurements [1],[2]. Such a device will be very useful for the optimization of a variety of beamlines, such as high current linacs, bunch rotators and storage rings. The signal from a non-axial trajectory or a tilted beam is in quadrature to that observed...

To achieve fast damping, the NLC Main Damping Ring uses a wiggler with high field strength, 2.15 T, and over 45 m in length. An ideal wiggler with infinitely wide pole pieces may be treated as a linear element, and has no impact on the dynamic aperture. However, the integrated nonlinear components from a real wiggler with integrated field over 100 Tm can be significant, and the choice of method...

antibiotics with a complex composition and structure and is produced by certain strains of Bacillus licheniformis and Bacillus subtilis. It is mainly active against Gram-positive bacteria. Bc consists of a mixture of structurally similar polypeptides from 12 amino acids (AA). The most important and known component is Bc A (Fig. 1). Other important components are B1, B2 and B3 which together wit...

in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

The asymmetric unit of the title compound, C(25)H(31)NO(4), contains two independent mol-ecules. In one mol-ecule, the benzene ring and an attached meth-oxy group were refined as disordered over two sets of sites in a 0.65 (4): 0.35 (4) ratio. In both mol-ecules, the central ring of the acridinedione system adopts a flattened boat conformation. The four essentially planar atoms of this ring [ma...

In the title compound, C(20)H(13)NO, the indene ring is disordered over two sites with an occupancy ratio of 0.557 (2):0.443 (2). Both disordered components of indene are nearly perpendicular to the naphthalene ring system, making dihedral angles of 90.9 (2) and 85.0 (5)°. The five-membered ring of the 1H-pyrrol-2(3H)-one adopts an envelope conformation with the spiro C atom at the flap positio...