We study the spectrum $\{\lambda_j(m)\}_{j=1}^{\infty}$ of a timelike Killing vector field $Z$ acting as differential operator $D_Z$ on Hilbert space solutions massive Klein-Gordon equation $(\Box_g + m^2) u = 0$ globally hyperbolic stationary spacetime $(M, g)$ with compact Cauchy hypersurface. The inverse mass $m^{-1}$ is formally like Planck constant in Schr\"odinger equation, and we give We...

This paper shows that the general hypersurface of degree ≥ 6 in projective four space cannot support an indecomposable rank two vector bundle which is Arithmetically CohenMacaulay and four generated. Equivalently, the equation of the hypersurface is not the Pfaffian of a four by four minimal skewsymmetric matrix.

This paper shows that the general hypersurface of degree ≥ 6 in projective four space cannot support an indecomposable rank two vector bundle which is Arithmetically CohenMacaulay and four generated. Equivalently, the equation of the hypersurface is not the Pfaffian of a four by four minimal skewsymmetric matrix.

A candidate for a realistic relativistic quantum theory is the hypersurface Bohm-Dirac model. Its formulation uses a foliation of space-time into space-like hypersurfaces. In order to apply the theory and to make contact with the usual quantum formalism, one needs a framework for the description of subsystems. The presence of spin together with the foliation renders the subsystem description mo...

Given a real-valued continuous function defined on n-dimensional Euclidean space, we construct a Khalimsky-continuous integer-valued approximation. From a geometrical point of view, this digitization takes a hypersurface that is the graph of a function and produces a digital hypersurface—the graph of the digitized function.

For a general hypersurface of degree d in projective n-space, if n ≥ d the spaces of 2-pointed rational curves on the hypersurface are rationally connected; thus the hypersurfaces are rationally simply connected. This paper proves stronger versions of theorems in [HS05].

In this paper, we study the hypersurface families with Smarandache curves in 4-dimensional Galilean space G 4 and give conditions for different to be parameter curve which generates is geodesic on a . Also, investigate three types of marching-scale functions one these hypersurfaces construct an example it.