Identical Rules Research Articles

Equivalence between mixed models and displacement models sing reduced integration

AbstractRelations between displacement models using reduced integration and hybrid mixed models based on the Hellinger–Reissner and the Herrmann principles have been investigated. Five different isoparametric elements are considered for the case of plane stress, plane strain and plate bending elasticity problems.It is proved that the following relations hold for both models, provided the number of terms of a polynomial expressing the stress or strain component in the formulation of the mixed models is equal to the number of integration points of the reduced integration. If the stiffness matrix of the mixed model is evaluated by the identical integration rule with the reduced integration, the stiffness matrices of both models are identical. Thus, both models are equivalent, if the stiffness matrix of the mixed model is integrated exactly by the identical integration rule with the reduced integration.The displacement models using uniform reduced integration and selective reduced integration are equivalent to the mixed models based on the Hellinger–Reissner and the Herrmann principles except for the 6‐node element, respectively.

A dyadic determinant function

This paper proposes to define a dyadic determinant function as the n-th exterior power of an array. When the array is a square matrix and n is its row (or column) number, we obtain as a limit case the usual monadic determinant function. This approach provides a natural definition of the determinant of a non-square array as used in Lagrange's identity or Laplace's rule of expanding determinant. On the other hand, the successive exterior powers of a matrix provide a direct means of computing the coefficients of its characteristic polynomial.

Propensity rules for rotationally inelastic collisions of symmetric top molecules or linear polyatomic molecules with structureless atoms

Using an asymptotic expansion of the angular momentum coupling coefficients which appear in the infinite-order-sudden formulation of collisions between symmetric top molecules and structureless atoms [S. Green, J. Chem. Phys. 70, 816 (1979)], we demonstrate that in certain cases, transitions which conserve the ’’parity index’’ of the rotational wave function will be strongly favored over those in which the parity index changes. This propensity rule will apply both to transitions which are inelastic in J but elastic in K, the projection of J along the molecular axis, as well as to transitions which are elastic in J but inelastic in K. Identical propensity rules will emerge within a Born treatment of the collision dynamics. These rules are completely general and independent of the particular form of the atom–molecule potential. The propensity toward conservation of the parity index will also be apparent in collisions of slightly asymmetric tops and l-doubled linear polyatomic molecules. A simple criteria is developed to determine the minimum value of J for which these propensity rules will be valid. Examination of accurate close-coupling and coupled-states cross sections for the NH3–He and H2CO–He systems confirms the accuracy of the new propensity rules. These rules can be used to predict intensity changes in four-level double resonance experiments; excellent agreement is obtained in a comparison with available experimental data for collisions of both HCN and NH3 with He, Ar, Xe, and H2.

Composition Rules for Probabilities from Paired Comparisons

Let $P_{ab}$ be the probability that the outcome of a paired comparison involving $a$ and $b$ is favorable to $a$. This paper discusses composition rules that generate $p_{ac}$ given $p_{ab}$ and $p_{bc}$. The basic properties of composition rules are developed via an axiomatic approach. If $p_{ab} = F(w_a - w_b)$, where $F$ is a distribution function for a distribution that is symmetric about zero, then the paired comparison model is a linear model that is based on the distribution function $F$. It is shown that given any composition rule, which obeys certain basic axioms, there exists a linear model that generates an identical composition rule. The behavior of the composition rules are used to place a partial ordering on the paired comparison models and in particular on the linear models. This partial ordering is denoted as the extreme partial ordering. It is shown that linear models based on distributions with short tails tend to be more extreme than those based on distributions with long tails. The resulting partial ordering includes the result that the Thurstone-Mosteller model is more extreme than the Bradley-Terry model. The extreme ordering can also be used to place a partial ordering on distributions according to the lengths of their tails. The relation of this ordering to the $s$-ordering and $r$-ordering is examined.

Symmetric team problems and multi access wire communication

In this paper we deal with the problem of sharing one communication wire among a (possibly large) number of communication stations. The fact that all communication stations are considered identical and that they share one objective of using the communication wire as efficiently as possible leads to the concept of symmetric team problems. For symmetric team problems we define a symmetric solution by the restriction that all decision makers must have identical decision rules. In the first section of this paper the concepts of symmetric team problems and symmetric solutions are developed and motivated. A theorem is given that relates symmetric solutions to randomized decision rules. An example is given which illustrates that the concept of symmetric solutions explains some everyday phenomena. In the second section the access problem in multi-access wire communication is considered as a symmetric team problem. It is shown that the symmetric solution, which corresponds to randomized access rules, tends to give as good performance as the unrestricted solution when the number of stations becomes large (asymptotic optimality). The solutions are also determined numerically, giving quantitative information on the asymptotic behavior.

Non-Uniqueness of Determination of Molecular Weight Distribution Dependence of Properties by Blending Experiments

It is shown that in general blending experiments alone do not determine unique relations for the dependence of polymer properties upon molecular weight distribution. In particular, two theoretical expressions for the steady shear elastic compliance of molten polymer lead to identical property blending rules.

British History: A Plea for a New Subject

INTRODUCTORY NOTE.-J. C. Beaglehole, of the Victoria University of Wellington, was until his death in 1970 the doyen of New Zealand historians and-together with J. W. Davidson of the Australian National University, who died in 1973-a leader in developing historical consciousness and historiography in the South Pacific world area. His editions of the journals of Captain Cook and his Life of Captain James Cook (published in 1974 by Stanford University Press) are not only masterpieces of scholarship and insight into the eighteenth century but unrivaled in their penetration of oceanic, as well as merely maritime, history. The New Zealand Historical Association maintains an annual lecture in his memory, and the essay which follows was originally delivered as the first Beaglehole Memorial lecture when that association met at the University of Canterbury in May 1973. It was subsequently printed in the New Zealand Journal of History (vol. 8, no. 1, April 1974) and is republished here with minor alterations by the generous permission of that journal's editors. What follows is a modified version of an essay in historical restatement, which owes much to John Beaglehole's own vision and his understanding of what vision is.

有意味学習の実験的研究 III

The present experiment was designed to test the following hypothesis: When meaningfully learnable materials have been incomplete by learned and equivalence between new materials and the stored information has not yet been realized, inserted learning of the new materials which can be subsumed meaningfully by an identical transformation rule may facilitate retention of the original learning.Three lists of ten paired associates were presented (See Tables 1 & 2); the stimulus term was always a word and the response term consisted of nonsense syllables (NS), one to three in number with connectives. 43 college students served as Ss and were divided into experimental (M) and control (R) groups. Both groups learned List 1, being followed by List 3. Group M was then asked to learn List 2 while group R was required List 2′. All items in List 2 and half of List 3 (3a) can be learned meaningfully after rote learning of List 1. List 2′ and the other half of List 3 (3b) require rote learning.The effect of inserted learning was assessed by comparing Ss' performance on tests of List 3 before and after the learning of List 2 or 2′. When S's responses to individual items were classified into four categories (perfect; all three NS correct, but one or more errors in order or in connective(s); incorrect NS; no answer) only experimental Ss who had learned meaningful List 2 showed improvement in List 3a (See Tables 3 & 5). When responses were classified into six or more sensitive categories, the performances of both group Ss showed improvement. Performance in 3b, which had been much lower than that in 3a, showed no improvement in either case.

Rated similarity of high m CVC trigrams and words and low m CCC trigrams

Groups of 60 Ss rated pairs of low m CCC trigrams, pairs of high m trigrams or pairs of three-letter words for formal similarity on a scale from 0 to 100. Mean ratings showed a close correspondence to the letter-position identity rule relating a pair of items.