We brieey present a rigorous and modular method, we are developing to design concurrent systems starting from their desired properties. This method is based on a mechanization of Manna-Pnueli's modular validity concept and on a modular temporal language in which properties are invariant under stuttering 1]. A compositional proof system is established to support both speciication veriica-tion an...

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...

A general mobile modular manipulator can be defined as a m-wheeled holonomic/nonholonomic mobile platform combining with a n-degree of freedom modular manipulator. This paper presents a sliding mode adaptive neural-network controller for trajectory following of nonholonomic mobile modular manipulators in task space. Dynamic model for the entire mobile modular manipulator is established in consi...

More than forty years ago, Igusa proved in [Ig] a “Fundamental Lemma”, according to which, theta constants give an explicit generically injective map from some modular varieties related to the symplectic group Sp(n,R) into a projective space. The embedded varieties satisfy some quartic relations, the so called Riemann’s relations. We expect that similar results hold for orthogonal instead of sy...

(an 2 1 Fp) of such a form, μ is given by qd=dq: It lifts, by the same formula, to the space of p-adic modular forms. This suggests a relation with the Tate twist of the mod p Galois representation attached to f; if the latter is a Hecke eigenform. Over C; this operator has been considered already by Ramanujan, where it fails to preserve modularity “by a multiple of E2": Maass modi...ed it so t...

Symplectic modular invariance of the bosonic string partition function has been verified at genus 2 and 3 using the period matrix coordinatization of moduli space. A calculation of the transformation of the holomorphic part of the differential volume element shows that an extra phase arises together with the factor associated with a specific modular weight; the phase is cancelled in the transfo...

Let V be a representation of the modular group Γ of dimension p. We show that the Z-graded space H(V ) of holomorphic vector-valued modular forms associated to V is a free module of rank p over the algebra M of classical holomorphic modular forms. We study the nature of H considered as a functor from Γ-modules to graded M-lattices and give some applications, including the calculation of the Hil...

Hitherto the duality between left-to-right and right-to-left exponentiation algorithms has been a loosely defined concept. Recently, the author made the definition precise by adding requirements on space usage and operation types. Here it is shown that the Montgomery and Joye powering ladders are dual in this sense. Several versions of these algorithms are derived naturally with a cost-free, na...

Some of the consequences of Eyvind Wichmann’s contributions to modular theory and the QFT phase-space structure are presented. In order to show the power of those ideas in contemporary problems, I selected the issue of algebraic holography as well as a new nonperturbative constructive approach (based on the modular structur of wedge-localized algebras and modular inclusions) and show that these...