scholarly journals A Second-Order Theory of the Galilean Satellites of Jupiter

1978 ◽  
Vol 41 ◽  
pp. 209-236
Author(s):  
S. Ferraz-Mello
Keyword(s):  
Order Theory ◽  
Second Order ◽  
The Other ◽  
Reference Plane ◽  
Internal Mass ◽  
Galilean Satellites ◽  
Satellites Of Jupiter ◽  
Trigonometric Solution ◽  
The Mean ◽  
Non Linear Mechanics

AbstractThe theory of the motion of the Galilean satellites of Jupiter is developed up to the second-order terms. The disturbing forces are those due to mutual attractions, to the non-symmetrical internal mass distribution of Jupiter and to the attraction from the Sun. The mean equator of Jupiter is taken as the reference plane and its motion is considered. The integration of the equations is performed. The geometric equations are solved for the case in which the amplitude of libration is zero. The perturbation method is shortly commented on the grounds of some recent advances in non-linear mechanics.In a previous paper (Ferraz-Mello, 1974) one perturbation theory has been constructed with special regard to the problem of the motion of the Galilean satellites of Jupiter. In this problem, the motions are nearly circular and coplanar; on the other hand the quasi-resonances lead to strong perturbations. The main characteristic of the theory is that it allows the main frequencies to be kept fixed from the earlier stages, and so, to have a purely trigonometric solution.

scholarly journals On the Theory of the Galilean Satellites of Jupiter

1974 ◽  
Vol 62 ◽  
pp. 167-184
Author(s):  
S. Ferraz-Mello
Keyword(s):  
Closed Form ◽  
Linear Equations ◽  
First Integral ◽  
Order Theory ◽  
Radius Vector ◽  
Second Order ◽  
Galilean Satellites ◽  
Satellites Of Jupiter

In this communication the main equations for the variables: radius vector, longitude, P and Q (variables built from Laplace's perihelium first integral) are given in closed form. These equations are used for deriving the equations of a second-order theory. At this order, the equations for P and Q, are separated and they are integrodifferential linear equations. The equations for the radius vector and for the longitudes, give, after integration, perturbations which are purely trigonometric. The solution shows the features observed in the motion of Jupiter's Galilean satellites. The results are discussed, and extended to include the space variables.

Do children understand that people selectively conceal or express emotion?

2014 ◽  
Vol 39 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Hajimu Hayashi ◽  
Yuki Shiomi
Keyword(s):  
First Graders ◽  
Negative Emotion ◽  
Fifth Graders ◽  
Order Theory ◽  
Third Graders ◽  
Second Order ◽  
The Other ◽  
The Real ◽  
Express Emotion ◽  
Negative Feelings

This study examined whether children understand that people selectively conceal or express emotion depending upon the context. We prepared two contexts for a verbal display task for 70 first-graders, 80 third-graders, 64 fifth-graders, and 71 adults. In both contexts, protagonists had negative feelings because of the behavior of the other character. In the prosocial context, children were instructed that the protagonist wished to spare the other character’s feelings. In contrast, in the real-emotion context, children were told that the protagonist was fed up with the other character’s behavior. Participants were asked to imagine what the protagonists would say. Adults selected utterances with positive or neutral emotion in the prosocial context but chose utterances with negative emotion in the real-emotion context, whereas first-graders selected utterances with negative emotion in both contexts. In the prosocial context, the proportion of utterances with negative emotion decreased from first-graders to adults, whereas in the real-emotion context the proportion was U-shaped, decreasing from first- to third-graders and increasing from fifth-graders to adults. Further, performance on both contexts was associated with second-order false beliefs as well as second-order intention understanding. These results indicate that children begin to understand that people selectively conceal or express emotion depending upon context after 8 to 9 years. This ability is also related to second-order theory of mind.

The monadic theory of ω2

1983 ◽  
Vol 48 (2) ◽  
pp. 387-398 ◽  
Author(s):  
Yuri Gurevich ◽  
Menachem Magidor ◽  
Saharon Shelah
Keyword(s):  
Order Theory ◽  
Second Order ◽  
The Other ◽  
Weakly Compact ◽  
Compact Cardinal ◽  
Monadic Theory ◽  
Weakly Compact Cardinal

AbstractAssume ZFC + “There is a weakly compact cardinal” is consistent. Then:(i) For every S ⊆ ω, ZFC + “S and the monadic theory of ω2 are recursive each in the other” is consistent; and(ii) ZFC + “The full second-order theory of ω2 is interpretable in the monadic theory of ω2” is consistent.

Decidability and undecidability of theories with a predicate for the primes

1993 ◽  
Vol 58 (2) ◽  
pp. 672-687 ◽  
Author(s):  
P. T. Bateman ◽  
C. G. Jockusch ◽  
A. R. Woods
Keyword(s):  
General Result ◽  
Order Theory ◽  
Second Order ◽  
The Other ◽  
Linear Case ◽  
Natural Numbers ◽  
Successor Function ◽  
First Order ◽  
First Order Theory

AbstractIt is shown, assuming the linear case of Schinzel's Hypothesis, that the first-order theory of the structure 〈ω; +, P〉, where P is the set of primes, is undecidable and, in fact, that multiplication of natural numbers is first-order definable in this structure. In the other direction, it is shown, from the same hypothesis, that the monadic second-order theory of 〈ω S, P〉 is decidable, where S is the successor function. The latter result is proved using a general result of A. L. Semënov on decidability of monadic theories, and a proof of Semënov's result is presented.

SECOND ORDER NUCLEAR QUADRUPOLE EFFECTS IN SINGLE CRYSTALS: PART II. EXPERIMENTAL RESULTS FOR SPODUMENE

1953 ◽  
Vol 31 (5) ◽  
pp. 837-858 ◽  
Author(s):  
H. E. Petch ◽  
N. G. Cranna ◽  
G. M. Volkoff
Keyword(s):  
Principal Axis ◽  
Order Theory ◽  
Resonance Absorption ◽  
Second Order ◽  
The Other ◽  
Oxygen Ion ◽  
Principal Axes ◽  
Nuclear Quadrupole ◽  
Spin Determination ◽  
Resonance Absorption Line

Experiments on the splitting of the Al27 resonance absorption line in a single crystal of LiAl(SiO3)2 (spodumene) are described, and are used to illustrate the second order theory of Part I. [Formula: see text] for Al27 nuclei in spodumene is found to be 2950 ± 20 kc./sec. [Formula: see text] at Al sites is found to be 0.94 ± 0.01. The x principal axis (corresponding to the smallest eigenvalue [Formula: see text]) of [Formula: see text] at the Al sites is found to coincide with the b axis of the monoclinic spodumene crystal. The other two principal axes lie in the ac plane with the y axis (corresponding to the intermediate eigenvalue [Formula: see text]) making an angle of [Formula: see text] with the crystal c axis towards the a axis. The y principal axis at the Al sites and the z principal axis at the Li sites appear to point at the projection of the nearest oxygen ion in each case. The new method of spin determination proposed in Part I is checked by confirming the known value I = 5/2 for Al27.

scholarly journals New constants for Sampson-Lieske theory of the Galilean satellites of Jupiter from mutual occultation data

1996 ◽  
Vol 172 ◽  
pp. 145-150 ◽  
Author(s):  
R. Vasundhara ◽  
J.E. Arlot ◽  
P. Descamps
Keyword(s):  
Event Data ◽  
Galilean Satellites ◽  
Data Set ◽  
Secular Variations ◽  
Satellites Of Jupiter ◽  
The Mean ◽  
Occultation Data ◽  
Mutual Occultation

New constants for Sampson-Lieske theory of the Galilean Satellites have been derived using 6360 individual photographic positions (1891–1990) and 438 pseudo astrometric positions from mutual occultations during 1973, 1979, 1985 and 1991. Using these new sets of constants, significant improvement is noticed in the O-C values of the sky plane coordinates of the mutual event data set and residuals in longitude for Io and Europa are found to improve. Problems concerning the inclusion of mutual event data in attempting evaluation of secular variations of the mean motions of the satellites are discussed.

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