The Hilbert modular fourfold determined by the totally real quartic number field k is a desingularization of a natural compactification of the quotient space Γk\H, where Γk = PSL2(Ok) acts on H4 by fractional linear transformations via the four embeddings of k into R. The arithmetic genus, equal to one plus the dimension of the space of Hilbert modular cusp forms of weight (2, 2, 2, 2), is a bi...

Robots are needed to perform important field tasks such as hazardous material clean-up, nuclear site inspection, and space exploration. Unfortunately their use is not widespread due to their long development times and high costs. To make them practical, a modular design approach is proposed. Prefabricated modules are rapidly assembled to give a low-cost system for a specific task. This paper de...

We introduce the finite ring S2m = Z2m + iZ2m . We develop a theory of self-dual codes over this ring and relate self-dual codes over this ring to complex unimodular lattices. We describe a theory of shadows for these codes and lattices. We construct a gray map from this ring to the ring Z2m and relate codes over these rings, giving special attention to the case when m = 2. We construct various...

The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Γ, generated by monodromies of the periods ofX . This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H(X). We show that, depending on the choice of polarization, the genus g topological string amplitude is either a holomorphic quasi-modular ...

This work presents a modular technique for minimizing a deterministic nite state ma chine FSM while preserving its equivalence to the original system Being modular the minimization technique should consume less time and space Preserving equivalence the resulting minimized model can be employed in both temporal logic model checking and sequential equivalence checking thus reducing their time and...

An architecture and conceptual design for a robotically assembled, modular space telescope (RAMST) that enables extremely large space telescopes to be conceived is presented. The distinguishing features of the RAMST architecture compared with prior concepts include the use of a modular deployable structure, a general-purpose robot, and advanced metrology, with the option of formation flying. To...

This paper shows how two of the most important analysis methods for Petri nets can be performed in a modular way. We illustrate our techniques by means of modular Place/Transitions nets (modular PT-nets) in which the individual modules interact via shared places and shared transitions. For place invariants we show that it is possible to construct invariants of the total modular PT-net from inva...

We define Hilbert–Siegel modular forms and Hecke “operators” acting on them. As with Hilbert modular forms (i.e. with Siegel degree 1), these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying groups), modulo natural identifications we can make between certain spaces. With Hilbert–Siegel forms (i.e. with arbitrary Siegel d...

An overview is given of what mathematical physics can currently say about the vacuum state for relativistic quantum field theories on Minkowski space. Along with a review of classical results such as the Reeh–Schlieder Theorem and its immediate and controversial consequences, more recent results are discussed. These include the nature of vacuum correlations and the degree of entanglement of the...