We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor Tμν(gαβ, ∂τgαβ, ∂τ∂σgαβ , . . . , ) constructed from sums of terms the involving contractions of the metric and powers of arbitrary covariant derivatives of th...

It is generally accepted that, around the turn of the century, GIBBS and EINSTEIN independently developed two equivalent formulations of statistical mechanics. GIBBS’ version is taken as genuine and rigorous, while EINSTEIN’s, despite some features which are characteristic of him, is usually considered a not totally satisfactory attempt. It will be shown in the present work that such a picture ...

In this expository article we review the problem of finding Einstein metrics on compact Kähler manifolds and Sasaki manifolds. In the former half of this article we see that, in the Kähler case, the problem fits better with the notion of stability in Geometric Invariant Theory if we extend the problem to that of finding extremal Kähler metrics or constant scalar curvature Kähler (cscK) metrics....

In the article is examined the liquid-drop model of electron and atom, which assumes existence of electron both in the form the ball-shaped formation and in the form liquid. This model is built on the same principles, on which was built the liquid-drop model of nucleus, proposed by Bohr and Weizsacker. The keywords: electron, the liquid-drop model of nucleus.

T φ(At)dμ(t) for every linear functional φ in the norm dual A of A; cf. [3, Section 4.1]. Further, a field (φt)t∈T of positive linear mappings φ : A → B between C -algebras of operators is called continuous if the function t 7→ φt(A) is continuous for every A ∈ A. If the C-algebras include the identity operators, denoted by the same I, and the field t 7→ φt(I) is integrable with integral I, we ...

In this paper, we prove Kirchberg-type inequalities for any Kähler spin foliation. Their limiting-cases are then characterized as being transversal minimal Einstein foliations. The key point is to introduce the transversal Kählerian twistor operators.

Here we review the field of atom chips in the context of Bose-Einstein Condensates (BEC) as well as cold matter in general. Twenty years after the first realization of the BEC and 15 years after the realization of the atom chip, the latter has been found to enable extraordinary feats: from producing BECs at a rate of several per second, through the realization of matter-wave interferometry, and...

In this paper we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure-radiation type and that it restricts the spacetimes to Petrov types N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with...

The intuitionistic uncertain fuzzy linguistic variable can easily express the fuzzy information, and the power average (PA) operator is a useful tool which provides more versatility in the information aggregation procedure. At the same time, Einstein operations are a kind of various t-norms and t-conorms families which can be used to perform the corresponding intersections and unions of intuiti...

With the linear sigma model, we have studied Bose-Einstein condensation and the chiral phase transition in the chiral limit for an interacting pion system. A μ−T phase diagram including these two phenomena is presented. It is found that the phase plane has been divided into three areas: the Bose-Einstein condensation area, the chiral symmetry broken phase area and the chiral symmetry restored p...