The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyal-deformed multiplication with respect to the spatial variables. The Moyal-deformed multiplication corresponds to the product of the algebra of a Moyal plane described in the setting of spec...

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.

Recently there has been some renewed interest in Laguerre differential geometry [1], [2], [3]. This geometry was to a large extent developed by Blaschke and his school and a large amount of material about it can be found in [4]. Consider the set of oriented spheres in Euclidean space. If we add to this set the space of oriented planes, i.e. the spheres of infinite radii, then we obtain the spac...

This work proposes and study the concept of Functional Data Analysis transform, applying it to the performance improving of volumetric Bouligand-Minkowski fractal descriptors. The proposed transform consists essentially in changing the descriptors originally defined in the space of the calculus of fractal dimension into the space of coefficients used in the functional data representation of the...

The entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analogue of the Brunn-Minkowski inequality. Motivated by this connection to Convex Geometry, we survey various recent developments on forward and reverse entropy power inequalities not just for the Shannon-Boltzmann entropy but also more generally for Rényi entropy. In the proce...

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.