This paper outlines the construction of invariants of Hamiltonian group actions on symplectic manifolds. The invariants are derived from the solutions of a nonlinear rst order elliptic partial dierential equation involving the Cauchy-Riemann operator, the curvature, and the moment map (see (17) below). They are related to the Gromov invariants of the reduced spaces. Our motivation arises from the proof of the Atiyah-Floer conjecture in [17, 18, 19] which deals with the relation between holomorphic curves ! M S in the moduli space M S of at connections over a Riemann surface S and anti-self-dual instantons over the 4-manifold S. In [3] Atiyah and Bott interpret the space M S as a symplectic quotient of the space A S of connections on S by the action of the group G S of gauge transformations. A moment's thought shows that the various terms in the anti-self-duality equations over S (see equation (64) below) can be interpreted symplectically. Hence they should give rise to meaningful equations in a context where the space A S is replaced by a nite dimensional symplectic manifold M and the gauge group G S by a compact Lie group G with a Hamiltonian action on M . In this paper 2 we show how the resulting equations give rise to invariants of Hamiltonian group actions. The same adiabatic limit argument as in [19] then leads to a correspondence between these invariants and the Gromov{Witten invariants of the quotient M==G (Conjecture 3.6). This correspondence is the subject of the PhD thesis [27] of the second author. In Section 2 we review the relevant background material about Hamiltonian group actions, gauge theory, equivariant cohomology, and holomorphic curves in symplectic quotients. The heart of this paper is Section 3, where we discuss the equations and the...

this paper, now include cutting-plane capabilities as well as other ideas from the backlog of accumulated theory. As suggested by the title of this paper, the gap between theory and practice is indeed closing

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This paper presents theory and algorithms for the synthesis of standard C-implementations of speedindependent circuits. These implementations are block-level circuits which may consist of atomic gates to perform complex functions in order to ensure hazard-freedom. First, we present boolean covering conditions that guarantee the standard C-implementations operate correctly. Then, we present two algorithms that produce optimal solutions to the covering problem. The first algorithm is always applicable but does not complete on large circuits. The second algorithm, motivated by our observation that our covering problem can often be solved with a single cube, finds the optimal single-cube solution when such a solution exists. When applicable, the second algorithm is dramatically more efficient than the first, more general algorithm. We present results for benchmark specifications which indicate that our single-cube algorithm is applicable on most benchmark circuits and reduces run-times by ...

. Computer-Aided Software Engineering (CASE) tools encourage users to codify the specification for the design of a system early in the development process. They often use graphical formalisms, simulation, and prototyping to help express ideas concisely and unambiguously. Some tools provide little more than syntax checking of the specification but others can test the model for reachability of conditions, nondeterminism, or deadlock. Formal methods include powerful tools like automatic model checking to exhaustively check a model against certain requirements. Integrating formal techniques into the system development process is an effective method of providing more thorough analysis of specifications than conventional approaches employed by Computer-Aided Software Engineering (CASE) tools. In order to create this link, the formalism used by the CASE tool must have a precise formal semantics that can be understood by the verification tool. The CASE tool STATEMATE makes use of an...

We discuss generalizations of the Temperley-Lieb algebra in the Potts and XXZ models. These can be used to describe the addition of different types of integrable boundary terms. We use the Temperley-Lieb algebra and its one-boundary, two-boundary, and periodic extensions to classify different integrable boundary terms in the 2, 3, and 4-state Potts models. The representations always lie at critical points where the algebras becomes non-semisimple and possess indecomposable representations. In the one-boundary case we show how to use representation theory to extract the Potts spectrum from an XXZ model with particular boundary terms and hence obtain the finite size scaling of the Potts models. In the two-boundary case we find that the Potts spectrum can be obtained by combining several XXZ models with different boundary terms. As in the Temperley-Lieb case there is a direct correspondence between representations of the lattice algebra and those in the continuum conformal field theory. 1

Nested datatypes are a generalisation of the class of regular datatypes, which includes familiar datatypes like trees and lists. They typically represent constraints on the values of regular datatypes and are therefore used to minimise the scope for programmer error.

According to Atiyah-Bott [AB],[A] the moduli space of flat connections on a compact oriented 2-manifold with prescribed holonomies around the boundary is a finitedimensional symplectic manifold, possibly singular. A standard approach [W1, W2, V] to computing invariants (symplectic volumes, Riemann-Roch numbers, etc.) of the moduli

We obtain, using the Birman--Schwinger method, a series of necessary conditions for the existence of at least one bound state applicable to arbitrary central potentials in the context of nonrelativistic quantum mechanics. These conditions yield a monotonic series of lower limits on the `critical' value of the strength of the potential (for which a first bound state appears) which converges to the exact critical strength. We also obtain a sufficient condition for the existence of bound states in a central monotonic potential which yield an upper limit on the critical strength of the potential.

Single particles and jets in deeply inelastic scattering at low x are measured with the H1 detector in the region away from the current jet and towards the proton remnant, known as the forward region. Hadronic final state measurements in this region are expected to be particularly sensitive to QCD evolution effects. Jet crosssections are presented as a function of Bjorken-x for forward jets produced with a polar angle to the proton direction, ` jet , in the range 7 ffi ! ` jet ! 20 ffi . Azimuthal correlations are studied between the forward jet and the scattered lepton. Charged and neutral single particle production in the forward region are measured as a function of Bjorken-x, in the range 5 ffi ! ` ! 25 ffi , for particle transverse momenta larger than 1 GeV. QCD based Monte Carlo predictions and analytical calculations based on BFKL, CCFM and DGLAP evolution are compared to the data. Predictions based on the DGLAP approach fail to describe the data, except for those which a...