We rederive the w∞ Ward identities, starting from the existence of trivial linearized gauge invariances, and using the method of canceled propagators in the operator formalism. Recursion relations for certain classes of correlation functions are derived, and these correlation function are calculated exactly. We clarify the relation of these results with another derivation of the Ward identities...

Let X be a semi-stable arithmetic surface over the spectrum S of the ring of integers in a number field K. We assume that the generic fiber XK is geometrically irreducible and has positive genus. Consider a line bundle L on X , which is non-negative on every vertical fiber and equipped with an admissible metric (in the sense of Arakelov [A]) of positive curvature. In [S] we have shown that any ...

We study equivariant embeddings with small boundary of a given homogeneous space G/H, where G is a connected linear algebraic group with trivial Picard group and only trivial characters, and H ⊂ G is an extension of a connected Grosshans subgroup by a torus. Under certain maximality conditions, like completeness, we obtain finiteness of the number of isomorphism classes of such embeddings, and ...

The close relationship between the scheme of level structures on universal deformation a formal group and Morava E-cohomology finite abelian groups has played an important role in study power operations for E-theory. goal this paper is to explore p-divisible given by trivial extension constant iterated free loop space classifying group.

This paper focuses on the Ki-groups of two types extensions abelian categories, which are trivial extension and gluing categories. We prove that, under some conditions, a certian subcategory category is isomorphic to similar original category. Moreover, we show that left (right) categories direct sum As their applications, obtain results ring by bimodule (i∈N).

Solovay showed that there are noncomputable reals α such that H(α ↾ n) 6 H(1) + O(1), where H is prefix-free Kolmogorov complexity. Such H-trivial reals are interesting due to the connection between algorithmic complexity and effective randomness. We give a new, easier construction of an H-trivial real. We also analyze various computability-theoretic properties of the H-trivial reals, showing f...

We give a number field analogue of result Ramanujan, Hardy and Littlewood, thereby obtaining modular relation involving the non-trivial zeros Dedekind zeta function. also provide Riesz-type criterion for Generalized Riemann Hypothesis ζK(s). New elegant transformations are obtained when K is quadratic extension, one which involves modified Bessel function second kind.

We generalise Merzlyakov's theorem about the first-order theory of non-abelian free groups to all acylindrically hyperbolic groups. As a corollary, we deduce that if $G$ is an group and $E(G)$ denotes unique maximal finite normal subgroup $G$, then HNN extension $G\dot{\ast}_{E(G)}$, which simply product $G\ast\mathbb{Z}$ when trivial, have same $\forall\exists$-theory. consequence, prove follo...

Recently, finite state automata, via the advent of hyperbolic and automatic groups, have become a powerful tool in geometric group theory. This paper develops a geometric approach to automata theory, analogous to various techniques used in combinatorial group theory, to solve various problems on the overlap between group theory and monoid theory. For instance, we give a geometric algorithm for ...