We investigate the necessary conditions for two spacetimes, which are solutions to Einstein field equations with an anisotropic matter source, be related each other by means of a conformal transformation. As result, we obtain that if one such spacetimes is generalization Robertson-Walker solution vanishing acceleration and vorticity, then has in this class as well, i.e. factor will constant fun...

Empirical Similitude Method (ESM) is a technique developed to address the concerns of non – linear similitude. The process disconnects the scaling of material and shape response by assuming them to be independent to form a system transformation. Such a transformation requires modeling using three representative models instead of just one as is used in the Buckingham π theorem. In an effort to g...

The aim of this article is to develop the basics of a theory of constrained Willmore surfaces. These are the critical points of the Willmore functional W = ∫ H 2 dA restricted to the class of conformal immersions of a fixed Riemann surface. The class of constrained Willmore surfaces is invariant under Möbius transformations of the ambient space. Examples include all constant mean curvature surf...

We study a static massless minimally coupled scalar field created by a source in a static D-dimensional spacetime. We demonstrate that the corresponding equation for this field is invariant under a special transformation of the background metric. This transformation consists of the static conformal transformation of the spatial part of the metric accompanied by a properly chosen transformation ...

This paper presents a new computational method for identifying side faces of thin-walled solids that can be excluded from the first step of conformal transformation from a tet mesh to an all-hex mesh. By excluding such side faces, all-hex meshes created by the conformal transformation method better align with the boundary of the side faces and tend to exhibit better scaled Jacobian quality. The...

This paper studies geometrical structure of the manifold of escort probability distributions and shows its new applicability to information science. In order to realize escort probabilities we use a conformal transformation that flattens so-called alpha-geometry of the space of discrete probability distributions, which well characterizes nonadditive statistics on the space. As a result escort p...

We use C-algebras to study complex algebraic curves. Our approach is based on the representation of an algebraic curve of genus g by the interval exchange transformation due to H. Masur, W. Veech et al. We study the C-algebra Oλ connected to such transformation. The main result says that the algebra Oλ, taken up to Morita equivalence, defines the curve C, up to conformal equivalence. The first ...

Let D be a domain in the complex plane (Riemann sphere) and R(D) the totality of one-valued regular analytic functions defined in D. With the usual definitions of addition and multiplication R(D) becomes a commutative ring (in fact, a domain of integrity). A oneto-one conformai transformation f =0(z) of D onto a domain A induces an isomorphism ƒ—>ƒ* between R(D) and R(A):f(z) =ƒ*[(2)]. An an...

We investigate emergent holography of weakly coupled two-dimensional hyperKähler sigma model on T ∗CP. The sigma model is motivated by the spacetime conformal field theory dual to the near-horizon geometry of Q1 D1-brane bound to Q5 D5-brane wrapped on T × S, where N = Q1Q5. The sigma model admits nontrivial instantons for all N ≥ 2, which serves as a local probe of emergent holographic spaceti...

Quantization in the minisuperspace of non minimal scalar-tensor theories leads to a partial differential equation which is non separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form, which corresponds to the minimal coupling case, whose general solution is known. Performing the inverse conformal transformation in the solution so found, we c...