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...

In this paper we define an addition operation on the class of quasiconcave functions. While the new operation is similar to the well-known supconvolution, it has the property that it polarizes the Lebesgue integral. This allows us to define mixed integrals, which are the functional analogs of the classic mixed volumes. We extend various classic inequalities, such as the Brunn-Minkowski and the ...

We consider billiard systems within compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. derive conditions for elliptic periodicity such billiards. describe topology those terms Fomenko invariants. provide then functional Pell equations and related extremal polynomials. Several examples are computed functions classical Chebyshev Zolotarev polynomials,...

In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated. Keywords—Frenet Apparatus, Time-like Curves, Minkowski Space-time.

In this paper we study the geometry of Minkowski plane and obtain some results. We focus on the curve theory in Minkowski plane and prove that the total curvature of any simple closed curve equals to the total Landsberg angle. As the result, the sum of oriented exterior Landsberg angles of any polygon is also equal to the total Landsberg angle, and when the Minkowski plane is reversible, the su...

We prove a complete set of integral geometric formulas of Crofton type (involving integrations over affine Grassmannians) for the Minkowski tensors of convex bodies. Minkowski tensors are the natural tensor valued valuations generalizing the intrinsic volumes (or Minkowski functionals) of convex bodies. By Hadwiger’s general integral geometric theorem, the Crofton formulas yield also kinematic ...

In a recent paper with J. A. Wieacker it was shown that certain integral-geometric formulas of Crofton type for lower-dimensional areas carry over from Euclidean to Minkowski spaces, if the Holmes-Thompson notion of Minkowskian area is employed and the Minkowski spaces are of a special type, called hyperme-tric. Here we show rst that there exist Minkowski spaces for which, among all axiomatical...

General offset curves are treated in the context of Minkowski geometry, the geometry of the two-dimensional plane, stemming from the consideration of a strictly convex, centrally symmetric given curve as its unit circle. Minkowski geometry permits us to move beyond classical confines and provides us with a framework in which to generalize the notion of Pythagorean-hodograph curves in the case o...

In this paper we discuss about properties of lattices and its application in theoretical algorithmic number theory. This result Minkowski regarding the initiated subject Geometry Numbers, which uses geometry to study algebraic numbers. It has on various other fields mathematics especially Diophantine equations, analysis functional etc. will review all major developments that have occurred field...

5 Minkowski, R., Paris Symposium on Radio Astronomy, ed. R. N. Bracewell (Stanford: Stanford University Press, 1959), p. 315. 6 Oort, J. H., M. N., 106, 159 (1946); Problems of Cosmical Aerodynamics (Dayton: Central Air Documents Office, 1951), p. 118. 7 Baade, W., and R. Minkowski, Observatory, 74, 130 (1954). 8 Baade, W., and R. Minkowski, Ap. J., 119,206 (1954). 9Jennison, R. C., Paris Sympo...