The solutions of two-dimensional gravity following from a non– linear Lagrangian L = f(R)√g are classified, and their symmetry and singularity properties are described. Then a conformal transformation is applied to rewrite these solutions as analogous solutions of twodimensional Einstein-dilaton gravity and vice versa. KEY : Dilaton gravity in 1+1 dimensions, exact solutions, Birkhoff theorem, ...

The purpose is to formulate a Fourier transformation for the space of functionals, as an infinitesimal meaning. We extend R to ( ∗R) under the base of nonstandard methods for the construction. The domain of a functional is the set of all internal functions from a ∗-finite lattice to a ∗-finite lattice with a double meaning. Considering a ∗-finite lattice with a double meaning, we find how to tr...

Let G be the group of rational points of a connected reductive p-adic group and let K be a maximal compact subgroup satisfying conditions of Theorem 5 from Harish-Chandra (1970). Generalized spherical functions on G are eigenfunctions for the action of the Bernstein center, which satisfy a transformation property for the action of K. In this paper we show that spaces of generalized spherical fu...

The anomalous conformal transformation law of the generalized entropy is found for dilaton gravity coupled to a 1+1 conformal matter sector with central charges c = c̃. (When c 6= c̃ the generalized entropy is not invariant under local Lorentz boosts.) It is shown that a certain second null derivative of the entropy, S′′ gen + (6/c)(S ′ out) , is primary, and therefore retains its sign under a ge...

Deformations of surfaces with the same intrinsic shape can often be described accurately by a conformal model. A major focus of computational conformal geometry is the estimation of the conformal mapping that aligns a given pair of object surfaces. The uniformization theorem enables this task to be acccomplished in a canonical 2D domain, wherein the surfaces can be aligned using a Möbius transf...

It is argued that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a consequence, two dimensional conformal field theory techniques will play as fundamental a role in this context of direct ph...

Vertex algebras in higher dimensions correspond to models of Quantum Field Theory (Wightman axioms) with Global Conformal Invariance. We review how such a vertex algebra can be generated from a collection of local fields, or from a vertex Lie algebra. The one-dimensional restriction of a vertex algebra in higher dimensions to a time-like line gives a chiral vertex algebra endowed with an action...

A novel robust adaptive beamforming method for conformal array is proposed. By using interpolation technique, the cylindrical conformal array with directional antenna elements is transformed to a virtual uniform linear array with omni-directional elements. This method can compensate the amplitude and mutual coupling errors as well as desired signal point errors of the conformal array efficientl...