Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 ...

The recent discovery of super-Earths (masses ≤ 10 M⊕) has initiated a discussion about conditions for habitable worlds. Among these is the mode of convection, which influences a planet’s thermal evolution and surface conditions. On Earth, plate tectonics has been proposed as a necessary condition for life. Here we show, that super-Earths will also have plate tectonics. We demonstrate that as pl...

The recent discovery of super-Earths (masses ≤ ) has initiated a discussion about conditions for habitable 10 M worlds. Among these is the mode of convection, which influences a planet’s thermal evolution and surface conditions. On Earth, plate tectonics has been proposed as a necessary condition for life. Here we show that super-Earths will also have plate tectonics. We demonstrate that as pla...

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

The majority of discovered exoplanetary systems harbour a new class of planets, bodies that are typically several times more massive than the Earth but that orbit their host stars well inside the orbit of Mercury. The origin of these close-in super-Earths and mini-Neptunes is one of the major unanswered questions in planet formation. Unlike the Earth, whose atmosphere contains less than 10−6 of...

While the seismic quality factor and phase lag are defined solely by the bulk properties of the mantle, their tidal counterparts are determined by both the bulk properties and the size effect (self-gravitation of a body as a whole). For a qualitative estimate, we model the body with a homogeneous sphere, and express the tidal phase lag through the lag in a sample of material. Although simplisti...

It is shown that rare earths can be distributed between two immiscible ionic liquids, allowing the transfer of the rare earths from one ionic liquid phase to another. The ionic liquid 1-ethyl-3-methylimidazolium chloride was used as the initial feed phase and the ionic liquid trihexyl(tetradecyl)phosphonium bis(2,4,4trimethylpentyl)phosphinate (Cyphos IL 104) as the extracting phase. The rare e...

Linearization of the nonlinear equations and iterative solution is the most well-known scheme in many engineering problems. For geodetic applications of the LEO satellites, e.g. the Earth’s gravity field recovery, one needs to provide an initial guess of the satellite location or the so-called reference orbit. Numerical integration can be utilized for generating the reference orbit if a satelli...

While the recent microlensing discoveries of super-Earths orbiting two M dwarf stars have been taken as support for the core accretion mechanism of giant planet formation, we show here that these planets could also have been formed by the competing mechanism of disk instability, coupled with photoevaporative loss of their gaseous envelopes by a strong external source of UV radiation, i.e., an O...