We study the thermalization of smeared particle detectors that couple locally to any operator in a quantum field theory curved spacetimes. show if state satisfies Kubo-Martin-Schwinger condition with inverse temperature $\ensuremath{\beta}$ respect detector's local notion time evolution, reasonable assumptions ensure probe thermalizes $1/\ensuremath{\beta}$ limit long interaction times. Our met...

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.

Quite recently, an Orlicz Minkowski problem has been posed and the existence part of this problem for even measures has been presented. In this paper, the existence part of the Orlicz Minkowski problem for polytopes is demonstrated. Furthermore, we obtain a solution of the Orlicz Minkowski problem for general (not necessarily even) measures.

The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.

Klein and Kroll classified Minkowski planes with respect to subgroups of central automorphisms and obtained a multitude of types. Some of these types are known to exist only in finite Minkowski planes or as the type of a proper subgroup in the automorphism group. In this paper we investigate the Klein– Kroll types of flat Minkowski planes with respect to the full automorphism groups of these pl...

A Steiner type formula for continuous translation invariant Minkowski valuations is established. In combination with a recent result on the symmetry of rigid motion invariant homogeneous bivaluations, this new Steiner type formula is used to obtain a family of Brunn-Minkowski type inequalities for rigid motion intertwining Minkowski valuations.

In this paper we have provided the " Missing Link " between κ-Minkowski spacetime and Doubly Special Relativity (DSR). We have constructed a relativistic point particle Lagrangian that has the κ-Minkowski algebra as its symplectic structure and has the DSR dispersion relation as its energy spectrum. Thus a dynamical connection between κ-Minkowski spacetime and DSR framework has been established...