We modify and extend proofs of Serrin’s symmetry result for overdetermined boundary value problems from the Laplace-operator to a general quasilinear operator and remove a strong ellipticity assumption in [9] and a growth assumption in [5] on the diffusion coefficient A, as well as a starshapedness assumption on Ω in [4]. Mathematics Subject Classification (2000). 35J65, 35B35

G. Gaeta Department of Mathematics, Loughborough University, Loughborough LE11 3TU (G.B.) [email protected] G. Marmo Dipartimento di Scienze Fisiche, Universit a di Napoli, and INFN, Sezione di Napoli, 80123 Napoli (Italy) Summary. We consider the classical problem of linearizing a vector eld X around a xed point. We adopt a nonperturbative point of view, based on the symmetry properties of lin...

What is quantum geometry? This question is becoming a popular leitmotiv in theoretical physics and in mathematics. Conformal field theory may catch a glimpse of the right answer. We review global aspects of the geometry of conformal fields, such as duality and mirror symmetry, and interpret them within Connes’ non-commutative geometry.

Many classical results concerning quadratic forms have been extended to hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear forms without any symmetry property. The present paper will establish a Witt cancellation result, an analogue of Springer’s theorem, as well as some local-global and finiteness results in this context. Mathematics Subject C...

In this paper, we present the hidden symmetry behind the Faddeev-Reshetikhin-TakhtajanSemenov-Tian-Shansky realization of quantum affine superalgebras Uq( ˆ osp(1, 2)) and add the q-Serre relation to the Drinfeld realization of Uq( ˆ osp(1, 2)) [8] derived from the FRTS realization. Mathematics Subject Classifications (1991): 81R10, 17B37

In this paper the notion of symmetry for implicit generalized Hamiltonian systems will be studied and a reduction theorem, generalizing the ’classical’ reduction theorems of symplectic and Poisson Hamiltonian systems, will be derived. 1991 Mathematics Subject Classification: 70H33, 58F05, 70H05, 70F25, 34A09, 34C20, 34A05

We study strong maximum principles for singular solutions of nonlinear elliptic and degenerate elliptic equations of second order. An application is given on symmetry of positive solutions in a punctured ball using the method of moving planes. Mathematics Subject Classification (2000). 35J69, 58J05, 53C21, 35J60.

In this thesis, we will discuss Freiling’s axiom of symmetry from an intuitionistic point of view. Using Brouwer’s Continuity Principle and fan theorem, we will find that the natural interpretation of this axiom holds in intuitionistic mathematics. The same is true for most of the extensions formulated by Freiling, in so far as they have a natural interpretation in intuitionism.

We introduce osp(m|n) spin Calogero-Sutherland models and find that the models have the symmetry of osp(m|n) half-loop algebra or Yangian of osp(m|n) if and only if the coupling constant of the model equals to 2 m−n−4 . Mathematics Subject Classifications (2000): 70H06, 81R12, 17B70.

We review the classical Principle of the Least Action in a general context where the Hamilton function H is possibly non convex. We show how van Groesen [6] principle follow as particular cases where H is hyperregular and of homogeneous type. Homogeneous scalar field spacetimes in spherical symmetry are derived as an application. 2000 Mathematics Subject Classification. 70H03, 70H05, 70H30, 37J05.