We begin with historical remarks on the basic contributions to thermodynamics and statistics with some bias to scientists working in Berlin as Helmholtz, Clausius, Nernst and Einstein. We underline the key role of thermodynamic ideas in the scientific revolutions in the 20th century. Further we discuss several recent applications to natural, evolutionary and informational systems, exotic applic...

A left invariant metric on a nilpotent Lie group is called minimal, if it minimizes the norm of the Ricci tensor among all left invariant metrics with the same scalar curvature. Such metrics are unique up to isometry and scaling and the groups admitting a minimal metric are precisely the nilradicals of (standard) Einstein solvmanifolds. If N is endowed with an invariant symplectic, complex or h...

We report observations of vortex formation by merging and interfering multiple (87)Rb Bose-Einstein condensates (BECs) in a confining potential. In this experiment, a single harmonic potential well is partitioned into three sections by a barrier, enabling the simultaneous formation of three independent, uncorrelated BECs. The BECs may either automatically merge together during their growth, or ...

X iv :0 81 0. 19 24 v3 [ m at h. A G ] 7 F eb 2 00 9 EXTREMAL METRICS ON DEL PEZZO THREEFOLDS IVAN CHELTSOV AND CONSTANTIN SHRAMOV In memory of Vasily Iskovskikh Abstract. We prove the existence of Kähler–Einstein metrics on a nonsingular section of the Grassmannian Gr(2, 5) ⊂ P by a linear subspace of codimension 3, and the Fermat hypersurface of degree 6 in P(1, 1, 1, 2, 3). We also show that...

In the present paper we studied the properties of them−projective curvature tensor in LP-Sasakian, Einstein LP-Sasakian and η−Einstein LPSasakian manifolds.

We overview our recent theoretical studies on nonlinear atom optics of the Bose-Einstein condensates (BECs) loaded into optical lattices. In particular, we describe the band-gap spectrum and nonlinear localization of BECs in one- and two-dimensional optical lattices. We discuss the structure and stability properties of spatially localized states (matter-wave solitons) in 1D lattices, as well as...

We prove that the abscissas of Bohr and Rogosinski for ordinary Dirichlet series, mapping the right half-plane into the bounded convex domain G ⊂ C are independent of the domain G. Furthermore, we obtain new estimates about these abscissas. 1. Preliminaries Let us recall the theorem of H.Bohr [19] in 1914. Theorem 1.1. If a power series