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 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.

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.

Predicative Fragments of Frege Arithmetic

2004 ◽  
Vol 10 (2) ◽  
pp. 153-174 ◽  
Author(s):  
Øystein Linnebo
Keyword(s):  
Natural Number ◽  
Order Theory ◽  
Peano Arithmetic ◽  
Two Dimensions ◽  
Second Order ◽  
Order Logic ◽  
The Other ◽  
Hume’S Principle ◽  
Important Exception ◽  
Second Order Logic

AbstractFrege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume's Principle, which says that the number of Fs is identical to the number of Gs if and only if the Fs and the Gs can be one-to-one correlated. According to Frege's Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume's Principle, the other, with the underlying second-order logic—and investigates how much of Frege's Theorem goes through in various partially predicative fragments of FA. Theorem 1 shows that almost everything goes through, the most important exception being the axiom that every natural number has a successor. Theorem 2 shows that the Successor Axiom cannot be proved in the theories that are predicative in either dimension.

scholarly journals On circular sections of a quadric surface

2020 ◽  
pp. 59-68
Author(s):  
Alexandr Seliverstov ◽  
Keyword(s):  
Principal Axis ◽  
The Other ◽  
Triaxial Ellipsoid ◽  
Straight Line Passing ◽  
Geometric Problems ◽  
Principal Axes ◽  
Centrally Symmetric ◽  
Plane Passing ◽  
History Of ◽  
Line Passing

A brief overview of the history of conic sections is given. Circular sections of ellipsoids and hyperboloids with planes passing through the center of the surface are considered. In general, there are two such secant planes. Generalizing the concept that arose in rigid-body mechanics, a straight line passing through the center of an ellipsoid is called the Galois axis if the orthogonal plane intersects this ellipsoid along a circle. Let us consider the pencil of planes passing through the intermediate principal axis of a triaxial ellipsoid. Each section of an ellipsoid with such a plane is an ellipse, one of the axes of which coincides with the intermediate principal axis of the ellipsoid. When the secant plane rotates around the intermediate principal axis of the ellipsoid, the length of the other axis of the ellipse continuously changes, taking values between the lengths of the minor and major axes of the ellipsoid. Therefore, some such section is a circle whose diameter is the intermediate principal axis of the ellipsoid. A triaxial ellipsoid has two such sections. They transform into each other when mirrored relative to the plane passing through the intermediate and other principal axes of the ellipsoid. Both Galois axes are orthogonal to the intermediate principal axis of the triaxial ellipsoid, and for a non-sphere ellipsoid of rotation, both Galois axes coincide with one axis and are orthogonal to the other principal axes of the ellipsoid. A method for constructing Galois axes from the known principal axes of an ellipsoid is proposed. This construction serves as one of the natural examples of geometric problems. In addition, the Galois axis can be correctly defined not only for the ellipsoid (for which it was originally introduced), but also for some other classes of centrally symmetric surfaces, including hyperboloids.

scholarly journals Seven- and eight-year-old children’s deception in the conflict situation

2020 ◽  
Author(s):  
Ryoichi Watanabe
Keyword(s):  
Theory Of Mind ◽  
Order Theory ◽  
Second Order ◽  
Conflict Situation ◽  
The Other ◽  
Conflict Condition ◽  
The Individual ◽  
Individual Condition

Six-year-olds will deceive in the individual condition, only if a competitor exists; but not in the conflict condition, when a competitor and a cooperator both exist. Seven- and eight-year-olds acquire the second-order theory of mind (ToM2) related to sophisticated deception. However, it is not known whether children and adults resort to deception in the conflict condition; and if a relationship exists between deception and ToM2. Children (N = 34, range = [6; 7-8; 5]) and adults (N = 38, range = [18-24]) participated in two deception tasks: for self-benefit and for the other person’s benefit. Children also participated in a ToM2 task. Although adults deceived above chance levels, children deceived only for self-benefit. Furthermore, although there was no relationship between children’s deception and ToM2; children who passed the ToM2 task tended to deceive by denying or not responding. These findings suggest that 7- and 8-year-olds can deceive for self-benefit in the conflict condition without ToM2.

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