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The nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time. A nontrivial extension of the ordinary quantum mechanics is thus…
We study a class of mixed non-Gaussian entangled states that, whilst closely related to Gaussian entangled states, none-the-less exhibit distinct properties previously only associated with more exotic, pure non-Gaussian states.
The Gaia mission has revolutionized our view of the Milky Way and its satellite citizens. The field of Galactic Archaeology has been piecing together the formation and evolution of the Galaxy for decades, and we have made great strides,…
The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function.
The symmetric tensor power of graphs is introduced and its fundamental properties are explored. A wide range of intriguing phenomena occur when one considers symmetric tensor powers of familiar graphs. A host of open questions are…
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…
Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures - the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has…
We show relation between sign of Gaussian curvature of cuspidal edge and geometric invariants through types of singularities of Gauss map. Moreover, we define and characterize positivity/negativity of cusps of Gauss maps by geometric…
Visualizations such as bar charts, scatter plots, and objects on geographical maps often convey critical information, including exact and relative numeric values, using shapes. The choice of shape and method of encoding information is often…
A general framework is developed to investigate the properties of useful choices of stationary spacelike slicings of stationary spacetimes whose congruences of timelike orthogonal trajectories are interpreted as the world lines of an…
In this paper, we provide properties and applications of some special integer sequences. We generalize and give some properties of Pisano period. Moreover, we provide a new application in Cryptography and applications of some quaternion…
We study the evolution of convex complete non-compact graphs by positive powers of Gauss curvature. We show that if the initial complete graph has a local uniform convexity, then the graph evolves by any positive power of Gauss curvature…
The physics that is traditionally formulated in one--time-physics (1T-physics) can also be formulated in two-time-physics (2T-physics). The physical phenomena in 1T or 2T physics are not different, but the spacetime formalism used to…
We consider the problem of calculating the Gaussian curvature of a conical 2-dimensional space by using concepts and techniques of distribution theory. We apply the results obtained to calculate the Riemannian curvature of the 4-dimensional…
Supersymmetry remains compelling theory over 30 years in spite of lack of its discovery. It could be already near the corner our days, therefore present and upcoming experiments are crucial for constraining or even discovery of the…
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
We discuss the phenomenon of the smooth dynamical gravity induced crossing of the phantom divide line in a framework of simple cosmological models where it appears to occur rather naturally, provided the potential of the unique scalar field…
Over the last decade Galactic planetary nebula discoveries have entered a golden age due to the emergence of high sensitivity, high resolution narrow-band surveys of the Galactic plane. These have been coupled with access to complimentary,…
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications…
If the Euclidean norm is strongly concentrated with respect to a measure, the average distribution of an average marginal of this measure has Gaussian asymptotics that captures tail behaviour. If the marginals of the measure have…