ar X iv : 0 80 4 . 34 49 v 2 [ gr - q c ] 1 7 M ay 2 00 8 Noether symmetry in f ( R ) cosmology

ar X iv : 0 71 2 . 38 38 v 3 [ gr - q c ] 3 1 M ay 2 00 8 General Transformation Formulas for Fermi - Walker Coordinates

ar X iv : 0 70 5 . 45 49 v 1 [ gr - q c ] 3 1 M ay 2 00 7 Quantum - theoretical description of the cosmological constant as the zero - point energy

The present paper seeks to construct a quantum theory of the cosmological constant in which its presently observed very small value emerges naturally. Large scale cosmological observations over the past decade (see references cited in [1], and [2-4]) have provided data which are in accord with the simplest cosmological model LCDM (Λ + Cold Dark Matter) [4-7]. This model is governed by the homog...

ar X iv : 0 80 5 . 24 44 v 1 [ m at h . A G ] 1 6 M ay 2 00 8 Symmetry and holomorphy of the second member of the second Painlevé hierarchy

We study symmetry and holomorphy of the second member of the second Painlevé hierarchy P (2) II .

ar X iv : 0 70 5 . 46 61 v 1 [ m at h . A G ] 3 1 M ay 2 00 7 ALGEBRAIC CYCLES AND MUMFORD - GRIFFITHS INVARIANTS

Let X be a projective algebraic manifold and let CH(X) be the Chow group of algebraic cycles of codimension r on X, modulo rational equivalence. Working with a candidate Bloch-Beilinson filtration {F }ν≥0 on CH(X)⊗Q due to the second author, we construct a space of arithmetic Hodge theoretic invariants ∇J(X) and corresponding map φ X : Gr F CH(X)⊗Q → ∇J(X), and determine conditions on X for whi...

ar X iv : 0 80 5 . 47 38 v 1 [ he p - th ] 3 0 M ay 2 00 8 U ( 1 ) invariant Membranes and Singularities

A formulation of U(1) symmetric classical membrane motions (preserving one rotational symmetry) is given, and reductions to systems of ODE’s, as well as some ideas concerning singularities and integrability. Let me start by giving some particular example(s) of a 2-dimensonal (timelike, time periodic) extremal manifold M2 ⊂ R and 3-folds (singularities included) of vanishing mean curvature, in 4...