Domain Walls from M-branes

We discuss the vertical dimensional reduction of M-branes to domain walls in D=7 and D=4, by dimensional reduction on Ricci-flat 4-manifolds and 7-manifolds. In order to interpret the vertically-reduced 5-brane as a domain wall solution of a dimensionally-reduced theory in D=7, it is necessary to generalise the usual Kaluza-Klein ansatz, so that the 3-form potential in D=11 has an additional term that can generate the necessary cosmological term in D=7. We show how this can be done for general 4-manifolds, extending previous results for toroidal compactifications. By contrast, no generalisation of the Kaluza-Klein ansatz is necessary for the compactification of M-theory to a D=4 theory that admits the domain wall solution coming from the membrane in D=11.Comment: Latex, 9 pages, reference adde

T-duality and U-duality in toroidally-compactified strings

We address the issue of T-duality and U-duality symmetries in the toroidally-compactified type IIA string. It is customary to take as a starting point the dimensionally-reduced maximal supergravity theories, with certain field strengths dualised such that the classical theory exhibits a global $E_{n(n)}$ symmetry, where n=11-D in D dimensions. A discrete subgroup then becomes the conjectured U-duality group. In dimensions D\le 6, these necessary dualisations include NS-NS fields, whose potentials, rather than merely their field strengths, appear explicitly in the couplings to the string worldsheet. Thus the usually-stated U-duality symmetries act non-locally on the fundamental fields of perturbative string theory. At least at the perturbative level, it seems to be more appropriate to consider the symmetries of the versions of the lower-dimensional supergravities in which no dualisations of NS-NS fields are required, although dualisations of the R-R fields are permissible since these couple to the string through their field strengths. Taking this viewpoint, the usual T-duality groups survive unscathed, as one would hope since T-duality is a perturbative symmetry, but the U-duality groups are modified in D\le 6.Comment: Latex, 21 pages. References and discussion adde

Development of a Straw Tube Chamber with Pickup-Pad Readout

We have developed a straw tube chamber with pickup-pad readout. The mechanism for signal pickup, the size of the pickup signal, and the distribution of signals among neighboring pads are discussed. We have tested a prototype chamber in a beamtest at Brookhaven National laboratory and have measured chamber efficiencies in excess of 99%.Comment: 7 pages, 8 figures, 2 tables. Talk presented at DPF '99 Meeting, UCL

Attenuation of Persistent L∞-Bounded Disturbances for Nonlinear Systems

A version of nonlinear generalization of the L1-control problem, which deals with the attenuation of persistent bounded disturbances in L∞-sense, is investigated in this paper. The methods used in this paper are motivated by [23]. The main idea in the L1-performance analysis and synthesis is to construct a certain invariant subset of the state-space such that achieving disturbance rejection is equivalent to restricting the state-dynamics to this set. The concepts from viability theory, nonsmooth analysis, and set-valued analysis play important roles. In addition, the relation between the L1-control of a continuous-time system and the l1-control of its Euler approximated discrete-time systems is established

Multi-scalar p-brane solitons

In a previous paper \cite{lp}, supersymmetric $p$-brane solutions involving one dilatonic scalar field in maximal supergravity theories were classified. Although these solutions involve a number of participating field strengths, they are all equal and thus they carry equal electric or magnetic charges. In this paper, we generalise all these solutions to multi-scalar solutions in which the charges become independent free parameters. The mass per unit $p$-volume is equal to the sum of these Page charges. We find that for generic values of the Page charges, they preserve the same fraction of the supersymmetry as in their single-scalar limits. However, for special values of the Page charges, the supersymmetry can be enhanced.Comment: 15 pages, Latex, no figure