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We present results regarding the longitudinal migrations of cool stellar spots that exhibit remarkable oscillations and explore their possible causes. We conducted analyses using high-quality data from nine target systems of various spectral types, spanning from F to M, which were observed by the Kepler Satellite. The systems in which the behaviour of the spots was examined are as follows: KIC 4357272, KIC 6025466, KIC 6058875, KIC 6962018, KIC 7798259, KIC 9210828, KIC 11706658, KIC 12599700, and KIC 8669092. Basic stellar parameters were calculated from light curve analysis using the PHOEBE V.0.32 software, and light curves were modelled to obtain sinusoidal variations occurring out-of-eclipses phases, induced by rotational modulation. Subsequently, we calculated the minimum times of the obtained sinusoidal variations using the Fourier transform. The distributions of ${\theta}_{\min}$ corresponding to these minimum times over time were computed using linear fits to determine the longitudinal migrations of the spotted areas. We then compared the longitudinal migration periods with the stellar parameters found in the literature. In addition, we also found a secondary variation in the spot migrations apart from the linear models. Our results revealed that the longitudinal migration periods vary in relation to the $B-V$ colour index of the stars.
This chapter discusses the class of covariant quantum spaces, which admit a large symmetry group. This includes the four-dimensional fuzzy sphere, the four-dimensional fuzzy hyperboloid, and a near-realistic 3 + 1 dimensional cosmological FLRW quantum spacetime.
Noncommutative field theory is the analog of classical field theory on quantum spaces. We discuss both classical as well as quantum aspects of such field theories. In particular, a transparent understanding of the crucial phenomenon of UV/IR mixing is obtained using the novel tool of string modes. These exhibit the stringy nature of noncommutative field theory, and will play an important role in the following. In particular, noncommutative gauge theory is defined via Yang–Mills matrix models.
The basic properties of Lie groups and related concepts are collected. This includes a discussion of coadjoint orbits and their symplectic structure, which helps to understand the semi-classical origin of imortant quantum spaces discussed in later chapters.
The higher-spin gauge theory arising on 3 + 1 dimensional covariant quantum spacetime is elaborated in detail, including the full fluctuation spectrum and the no-ghost theorem.
Gravitational plane waves and their detection start the chapter off in parallel with electromagnetic plane waves and their detection. Geodesic deviation is reviewed and allows for a brief introduction to LIGO. The stress tensor source of radiation (and therefore, at least local, plane waves) and its conservation of energy and momentum are tied to the radiation solution of the linearized form of Einstein’s equation. A highlight is the role of gauge freedom in making gravitational plane waves physically relevant (by gauge fixing to reveal the underlying plus and cross polarizations). Power loss to gravitational radiation is discussed in the linearized limit by comparison with electric quadrupole radiation.
This chapter discusses the problem of de-quantization. Starting with some given quantum space defined through a matrix configuration, a general procedure is developed which allows to associate a manifold and further geometrical structure underlying the given quantum space.