Solution set on the natural satellite formation orbits under first-order earth's non-spherical perturbation

2005 ◽  
Vol 21 (5) ◽  
pp. 503-510 ◽  
Author(s):  
Humei Wang ◽  
Wei Yang ◽  
Junfeng Li
Keyword(s):  
Solution Set ◽  
Satellite Formation ◽  
Natural Satellite ◽  
First Order

scholarly journals Applications of Stieltjes Derivatives to Periodic Boundary Value Inclusions

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2142
Author(s):  
Bianca Satco ◽  
George Smyrlis
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Solution Set ◽  
First Order

In the present paper, we are interested in studying first-order Stieltjes differential inclusions with periodic boundary conditions. Relying on recent results obtained by the authors in the single-valued case, the existence of regulated solutions is obtained via the multivalued Bohnenblust–Karlin fixed-point theorem and a result concerning the dependence on the data of the solution set is provided.

scholarly journals Exploring formation scenarios for the exomoon candidate Kepler 1625b I

2020 ◽  
Vol 495 (4) ◽  
pp. 3763-3776 ◽  
Author(s):  
R A Moraes ◽  
E Vieira Neto
Keyword(s):  
Solar System ◽  
Satellite System ◽  
Minimum Amount ◽  
Tidal Evolution ◽  
Satellite Formation ◽  
Natural Satellite ◽  
In Situ Formation ◽  
Do So

ABSTRACT If confirmed, the Neptune-size exomoon candidate in the Kepler 1625 system will be the first natural satellite outside our Solar system. Its characteristics are nothing alike we know for a satellite. Kepler 1625b I is expected to be as massive as Neptune and to orbit at 40 planetary radii around a ten Jupiter mass planet. Because of its mass and wide orbit, this satellite was first thought to be captured instead of formed in situ. In this work, we investigated the possibility of an in situ formation of this exomoon candidate. To do so, we performed N-body simulations to reproduce the late phases of satellite formation and use a massive circumplanetary disc to explain the mass of this satellite. Our setups started soon after the gaseous nebula dissipation, when the satellite embryos are already formed. Also for selected exomoon systems, we take into account a post-formation tidal evolution. We found that in situ formation is viable to explain the origin of Kepler 1625b I, even when different values for the star–planet separation are considered. We show that for different star–planet separations the minimum amount of solids needed in the circumplanetary disc to form such a satellite varies, the wider is this separation more material is needed. In our simulations of satellite formation, many satellites were formed close to the planet, this scenario changed after the tidal evolution of the systems. We concluded that if the Kepler1625 b satellite system was formed in situ, tidal evolution was an important mechanism to sculpt its final architecture.

scholarly journals ON PERIODIC SOLUTIONS FOR FIRST-ORDER DIFFERENTIAL EQUATIONS INVOLVING THE DISTRIBUTIONAL HENSTOCK–KURZWEIL INTEGRAL

2012 ◽  
Vol 86 (2) ◽  
pp. 327-338 ◽  
Author(s):  
WEI LIU ◽  
GUOJU YE ◽  
YING WANG ◽  
XUEYUAN ZHOU
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Topological Structure ◽  
Solution Set ◽  
First Order ◽  
General Integral ◽  
Existence Of Periodic Solutions ◽  
First Order Differential Equations

AbstractThe purpose of this paper is to study the existence of periodic solutions and the topological structure of the solution set of first-order differential equations involving the distributional Henstock–Kurzweil integral. The distributional Henstock–Kurzweil integral is a general integral, which includes the Lebesgue and Henstock–Kurzweil integrals. The main results extend some previously known results in the literature.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Morphological studies of linear (AB)n multiblock copolymers and their blends

1992 ◽  
Vol 50 (1) ◽  
pp. 384-385
Author(s):  
Richard J. Spontak ◽  
Steven D. Smith ◽  
Arman Ashraf
Keyword(s):  
Electron Microscopy ◽  
Microphase Separation ◽  
Multiblock Copolymers ◽  
First Order ◽  
Morphological Studies ◽  
Transmission Electron ◽  
First Order Phase Transition ◽  
Covalently Bonded ◽  
Total Molecular Weight ◽  
First Order Phase

Block copolymers are composed of sequences of dissimilar chemical moieties covalently bonded together. If the block lengths of each component are sufficiently long and the blocks are thermodynamically incompatible, these materials are capable of undergoing microphase separation, a weak first-order phase transition which results in the formation of an ordered microstructural network. Most efforts designed to elucidate the phase and configurational behavior in these copolymers have focused on the simple AB and ABA designs. Few studies have thus far targeted the perfectly-alternating multiblock (AB)n architecture. In this work, two series of neat (AB)n copolymers have been synthesized from styrene and isoprene monomers at a composition of 50 wt% polystyrene (PS). In Set I, the total molecular weight is held constant while the number of AB block pairs (n) is increased from one to four (which results in shorter blocks). Set II consists of materials in which the block lengths are held constant and n is varied again from one to four (which results in longer chains). Transmission electron microscopy (TEM) has been employed here to investigate the morphologies and phase behavior of these materials and their blends.

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