It is demonstrated, that 't Hooft's renormalization scheme (in which the β-function has exactly the two-loop form) is generally in conflict with the natural physical requirements and specifies the type of the field theory in an arbitrary manner. It violates analytic properties in the coupling constant plane and provokes misleading conclusion on accumulation of singularities near the origin. It ...

Let g be an eigenform of weight k+2 on Γ0(p)∩Γ1(N) with p N . If g is non-critical (i.e. of slope less than k + 1), using the methods of [1, 20], one can attach a p-adic L-function to g which is uniquely determined by its interpolation property together with a bound on its growth. However, in the critical slope case, the corresponding growth bound is too large to uniquely determine the p-adic L...

We describe V G k for general groups in §2. These formulas were first written down by E. Verlinde [23] in the context of Conformal Field theory. The interest towards them in Algebraic Geometry stems form the fact that they give the Hilbert function of moduli spaces of principle bundles over projective curves. More precisely, let C be a smooth projective curve of genus g, and let MC be the modul...

It is demonstrated, that 't Hooft's renormalization scheme (in which the β-function has exactly the two-loop form) is generally in conflict with the natural physical requirements and specifies the type of the field theory in an arbitrary manner. It violates analytic properties in the coupling constant plane and provokes misleading conclusion on accumulation of singularities near the origin. It ...

E a r l y v i s u a l p rocess ing i s con jec tu red t o be almost e n t i r e l y domainindependent and d a t a d r i v e n ; however, h i g h l e v e l v i s i o n must e x p l o i t domain and o b j e c t s p e c i f i c c o n s t r a i n t s and methods, i n t e r m i n g l i n g d a t a d r i v e n and mode l -d r i ven r e c o g n i t i o n . We are concerned w i t h knowledge r e p r e ...

Graded-division algebras are building blocks in the theory of finite-dimensional associative graded by a group G. If G is abelian, they can be described, using loop construction, terms central simple graded-division algebras. On other hand, given finite abelian G, any G-graded-division algebra over field F determined, thanks to result Picco and Platzeck, its class (ordinary) Brauer isomorphism ...