We show that the " time " t s defined via spin clusters in the Ising model coupled to 2d gravity leads to a fractal dimension d h (s) = 6 of space-time at the critical point, as advocated by Ishibashi and Kawai. In the unmagnetized phase, however, this definition of Hausdorff dimension breaks down. Numerical measurements are consistent with these results. The same definition leads to d h (s) = ...

Definition 2. AFrobenius structure on a manifold H is a Frobenius structure on each tangent space TtH such that (1) The metric <,> is flat (∇ = 0) (2) The vector field 1 is covariantly constant (∇1 = 0) (3) The system of PDE’s ~∇ws = w ◦ s is integrable ∀~ 6= 0, where w and s are vector fields and ◦ denotes the Frobenius multiplication. In ∇-flat coordinates {t}, this means that the family of c...

BACKGROUND The tidal flat is one of the important components of coastal wetland systems in the Yellow River Delta (YRD). It can stabilize shorelines and protect coastal biodiversity. The erosion risk in tidal flats in coastal wetlands was seldom been studied. Characterizing changes of soil particle size distribution (PSD) is an important way to quantity soil erosion in tidal flats. METHOD/PRI...

This can be compared to the fact that a conformally flat manifold of dimension n > 2 is locally conformal to a region of the sphere of the same dimension. In twistor theory, it is well-known that an even dimensional conformally flat manifold has an integrable twistor space ([7], [6], [1], [3]). It is interesting, as an analogy, that a Bochner-Kähler manifold has integrable twistor spaces define...

Let K denote a closed odd-dimensional smooth manifold and let E be a flat vector bundle over K. In this situation the construction of Ray and Singer [RS] gives a metric on the determinant line of the cohomology detH(M ;E) which is a smooth invariant of the manifold M and the flat bundle E. (Note that if the dimension of K is even then the Ray-Singer metric depends on the choice of a Riemannian ...

Thegeodesic flowof theflatmetric on a torus isminimizing the polynomial entropy among all geodesic flows on this torus. We prove here that this properties characterises the flat metric on the two torus. Résumé Leflot géodésique desmétriques plates sur un toreminimise l’entropie polynomiale parmi tous les flots géodésique sur ce tore. On montre ici que cette propriété caractérise les métriques p...

I review the holographic techniques used to efficiently study models with Gauge-Higgs Unification (GHU) in one extra dimension. The general features of GHU models in flat extra dimensions are then reviewed, emphasizing the aspects related to electroweak symmetry breaking. Two potentially realistic models, based on SU(3) and SO(5) electroweak gauge groups, respectively, are constructed.

In this letter we present an idea which reconciles a homogeneous and isotropic Friedmann universe with a fractal distribution of galaxies. We use two observational facts: The flat rotation curves of galaxies and the (still debated) fractal distribution of galaxies with fractal dimension D = 2. Our idea can also be interpreted as a redefinition of the notion of bias.

Intersection sheaves are usually defined for a proper flat surjective morphism of Noetherian schemes of relative dimension d and for d + 1 invertible sheaves on the ambient scheme. In this article, the construction is generalized to the equidimensional proper surjective morphisms over normal separated Noetherian schemes. Applications to the studies on family of effective algebraic cycles and on...

On pseudo-Riemannian manifolds of even dimension n ≥ 4, with everywhere vanishing (Fefferman-Graham) obstruction tensor, we construct a complex of conformally invariant differential operators. The complex controls the infinitesimal deformations of obstruction-flat structures, and, in the case of Riemannian signature the complex is elliptic.