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This paper investigates a type of grammatical ill-formedness in English which is traceable to the repetition, under certain specified conditions, of present participles, e.g. the verb "continue" cannot occur with participles if it is in the present progressive. The solution to generalizing about ill-formedness of this type is by means of a derivational constraint which is formulated in such a way as to link certain features of remote structure to certain features of surface structure. The violation is not stated in terms of a restriction on transformations but rather as a static filter on the output of the syntactic component. This paper refines and formally states the requisite derivational constraint so that it is not too powerful. The author examines the consequences for linguistic theor y of postulating such a derivational constraint. The argument for using such a constraint, details on its development, and references are presented. (Author/VM)

This paper discusses the working principles that have grown out of the experiences of an architect and a psychologist working together as a planning team. According to the author, the true problem in planning and design is the prediction of behavior. Therefore, although the basic problems should be handled by the designer, a psychologist can employ his specific tools to advance the goals of a planning or design group. For example, a psychologist can make quantified measurements of behavior for programing functional requirements; utilize experimental techniques in evaluating particular design variables; and construct surveys, case studies, and similar measurements for the validation of planning criteria. (Author/MLF)

A ring R is called, according to [2], a left p.p. ring if any principal left ideal of R is projective. A ring which is left and right p.p. is called a p.p. ring.In this short note we shall give some additional remarks to A. Hattori [2]. In Proposition 1 we shall give a characterization of commutative p.p. rings, and in Proposition 3 we shall give a generalization of Proposition 17 and 18 in [2], which shows also that the modified torsion theory over commutative p.p. rings coincides with the usual torsion theory.

A generalization of the Laplace transformation is denned by means-of an infinite sum. A short list of transformation pairs is included and application is made to a finite difference equation with constant coefficients discussed by N. J. Durant (Phil. Mag. xxxvi. p. 569, Aug. 1945). Further application to finite difference equations with rational coefficients is suggested.

In his valuable paper, Dr. Vetter raises many interesting questions and offers several acute observations on them. I cannot deal with all the problems he touches on within the confines of my comment. I must therefore limit my remarks to a few selected topics. Among the wealth of material offered by Dr. Vetter’s paper I have chosen two subjects for special consideration. They are (1) the relevance of mathematical statistics to a logician’s work on induction - and vice versa - and (2) the problem of inductive generalization.

Publisher Summary Smale introduced a family of flows called Morse–Smale flows. Later in his survey, he posed the question of generalization of this idea to other Lie group actions. This chapter presents an introduction to a similar study for actions of the group. It also discusses the hyperbolic linear actions and invariant manifold theory.

In a recent paper 1 I stated that von Neumann had originated the suggestion for the use of Schur's canonical form for arbitrary matrices. I have since learned that the suggestion actually is due in the first instance to John Greenstadt, who brought it to von Neumann's attention. The history of this is rather interesting and was communicated to me in a letter from John Greenstadt, which I quote below. “The full story is, that the triangularization occurred to me early in 1953, after trying in vain to find a general iterative diagonalization procedure, even where one knew that it was possible to diagonalize (defective degeneracy being the impossible case). It seemed to me that one thing that made for the stability of the Jacobi method was the fact that all the elements in the transformation matrix were less than 1. A natural generalization embodying this requirement was to consider unitary transformations. Then, a quick check of Murnaghan's book showed that one could hope only to triangularize, but that this was always possible. “I did some hand calculations on this, and lo and behold! it converged in the few cases I tried. I then programmed it for the CPC and tried many other cases. For several months thereafter, Kogbetliantz, John Sheldon, and I tried to prove convergence, when the algorithm involved the sequential annihilation of off-diagonal elements. We (particularly Sheldon) tried many approaches, but with no hint of success. Finally, in the latter part of 1953, we decided to ask von Neumann, who was then a consultant for IBM, when he was in New York at our offices. “I had prepared a writeup describing the procedure, but von Neumann (rightly) didn't want to bother reading it, so I explained it to him in about two minutes. He spent the next 15 minutes thinking up all the approaches we had thought of in three or four months, plus a few ones—all, however, without promise. “At this point he decided that it was a nontrivial problem, and perhaps not worth it anyway, and immediately suggested minimizing the sum of squares of subdiagonal elements, which is, of course, the truly natural generalization of the Jacobi method. For the next 15 minutes he investigated the case when it would be impossible to make an improvement for a particular pivotal element and found that these cases were of measure zero. “I recoded my procedure for the 701 and tried many other matrices of various sizes. I myself never had a failure, but it has since been demonstrated that the method will indeed fail for a class of matrices. Hence, a proof is clearly impossible. However, I think a statistical proof is possible, along lines suggested by Kogbetliantz, which, however, I have not been able to find. I do not think von Neumann's variation of the method would fail. (However, it is more complicated and time consuming.)”

near a point solution xi ai (i 1, 1 *, n) when certain conditions are satisfied. In the present paper these conditions are replaced by less stringent ones; the methods of proof of certain existence theorems are very similar to those employed in the first paper, and these proofs are given here in an abbreviated forin. In addition, the asymptotic properties of certain trajectories are discussed by an extension of the methods of Bohl. On account of the more complicated form of certain quadratic forms which occur here, it has been convenient to leave undetermined certain constants which are determined explicitly in the first paper; this procedure, together with the algebraic method of transforming the canonical equations, reduces to a small amount the results common to both papers.

F(k) ={xkj x F}; F,=F; Fk= (Fk_l,F). Let (u, v, 0)=u, (u, v, 1)=(u, v), (u, v, n)=((u, v, n-1), v). Then Sanov [3] proved that (1. 1) (u, v, apa _1) p-a E F(p#)Fapa+?, /3 a = 1, 2, where p is a prime. In this paper, (1.1) is proved for the cases a= 1, 2; 3 arbitrary. A slight generalization of these results is also proved. Sanov's proof involved an investigation of ideals in a Lie Ring. In this paper, Hall's Collection Process will be used. The method also yields other formulas, e.g. (1.2) (u, v, p2 1)P' (E F2p2_pF(p) (1.3) (u, v, pa+l 1)p~l C F2pa+l paF(pl), a = 1 2, and can be used to produce numerous formulas of a similar nature. The author hopes that some of these formulas and/or the method may be of use in solving other group-theoretic problems. The author was unable to use the method to prove (1.1) for a =3. Note that for a=f = 1, (1. 1) becomes (1.4) (U, v, p 1) E F(p)Fv+1. (1.4) plays an important role in the theory of the Restricted Burnside Problem.

The analogies that exist between infinite series and infinite integrals are well known and have frequently served to indicate the extension of a theorem or a method from one of these domains of investigation to the other. According to a principle of generalization that has been formulated by E. H. Moore, the presence of such analogies implies the existence of a general theory which incltudes the central features of both the special theories.t It is the purpose of the present paper to develop the fundamental principles of that sectioll of this general theorv which contains as particular instances the theories of Cesaro and H6lder summability of divergent series and divergent integrals. Furthermore, the usefulness of the theory will be illustrated by proving a general theorem in it which includes as special cases the Knopp-Schnee-Ford theoremt with regard to the equivalence of the Cesaro and Holder means for summing divergent series, an analogous theorem due to Landau ? concerning divergent integrals, and a further new theorem with regard to the equivalence of certain generalized derivatives. The general theorem just mentioned can be extended to the case of multiple limits so as to include other new theorems, analogous to those referred to above, with regard to multiple series, multiple integrals, and partial derivatives. This extension, however, involves formulas that are considerably more complicated than in the case of simple limits. I shall therefore reserve it for a second paper, as I wish to avoid algebraic complexity in this first presentation of the general theory. Following the terminology introduced by E. H. Moore, we indicate the basis of our general theory as follows

A model's influence on the creative behavior of 120 fifth-grade children was studied in four variations. Separate groups observed a model who was either high or low in the fluency or flexibility creativity dimensions. Multivariate procedures were used to assess treatment effects upon children's fluency and flexibility measures collected on parallel and on a very different type of creative task. High model fluency was found to significantly increase child fluency and flexibility measures on the parallel task. A marginally significant increase in observer fluency was noted on the stringent generalization task. Contrary to predictions, increased model flexibility produced significant decreases in observer fluency and flexibility measures on both the parallel and stringent generalization tasks. (Author)

Research was conducted relevant to two questions: First, does generalized imitation reflect the child's failure to discriminate reinforced from non-reinforced occasions? Second, are the results which characterize generalized imitation a function of confounded social and instructional influences that operate within the procedures used in generalized imitation research? A generalized imitation experiment was conducted utilizing seven 9-year-old girls as Ss and two female graduate students as experimenter-models. Two kinds of trials were presented in each session. For the first four or five sessions, only successive-discrimination trials were presented. Following these sessions, each session contained blocks of successive-discrimination trials and blocks of choice trials. It is concluded that the generalized imitation may be the result of strong social and instructional variables. (CK)

Subject matter concept attainment by adult Ss was studied by experimentally manipulating instructional instances which were either positive or negative, clear or obscure, or presented in large or small variety. Training and testing instances were composed of case studies communicated via prose description that had been analyzed for relevant and irrelevant attributes. Conceptualization was defined as generalization within and discrimination between classes and was assessed by having 176 undergraduate volunteers classify new positive and negative case studies after instruction from a definition and selected instances. Two, three-way analyses of variance followed by t-tests revealed that instance type, identifiability, and variety have differential effects on generalization and discrimination. References are included. (Author)

In this paper guidelines which provide direction toward the development and structure of a course in social foundations of education are outlined. A systems approach to organization of the course is used as both a content and process guide. The construct of the parts of this education system defines four operational functions: 1) development of the specific goal of the system in our societal structure and of the specific enabling objectives; 2) an input category consisting of the key elements of our societal context which help define options for courses of action; 3) a strategy category which operates as the means used to achieve objectives; and 4) a teaching operation which functions to check on the efficiency and effectiveness of the educational organization and helps suggest necessary modifications. Theoretical models for developing course strategies are discussed and specific strategies--concepts and key phrases, persistent questions, and hypotheses and generalizations--actually being used in the author's social foundations of education courses are included. (SHM)

In this essay, research done on concept learning is discussed. The study analyzes concept learning as one form of learning, formulating guidelines for teaching concepts, and describes the abilities underlying the attainment of concepts. An analytical model is presented; various operations such as concrete concepts and identity concepts are described. Cognitive functions such as acquiring appropriate labels, remembering, and attending are discussed. Then, concept utilization and extension are discussed. The essay concludes with a consideration of the uses of the model just presented. (Author/JW)

In planning educational research, recognition needs to be made of five domains of learning: (1) motor skills, (2) verbal information, (3) intellectual skills, (4) cognitive strategies, and (5) attitudes. In being cognizant of these domains, the researcher is able to distinguish the parts of a content area which are subject to different instructional treatment. He becomes better able to relate the instructional procedures of one subject to those of another. Also, in identifying domains of learning, he recognizes that each requires different techniques for assessment of learning outcomes. Although the five domains are the primary categories which limit the generalizability of conclusions about the learning process, other very obvious characteristics impose limitations as well. Sex and race have been extensively analyzed as have environmental and cultural differences. Age deserves further consideration to show not only what the differences in learning are but why they may be expected to occur. Because the process of learning for a student at one age is likely to be very different from that of a student of another age, differential plans for different ages becomes of critical importance. Clear thinking about the process of learning will be enhanced when researchers recognize necessary distinctions about learning that define the limits within which generalizations can and should be made. (WY)

The "Flash Lab" method of teaching the elementary fundamentals of drawing, a system based on the psychology of perception, the behavioral sciences, and the biological sciences, was developed to help correct common errors which beginning students make, such as inability to generalize, lack of proportional relationships, misjudgement due to depth, poor brightness discrimination, and little sense of unity or composition. The 16-week "Flash Lab" program is divided into three major phases (the Flash Phase, the Transitional Phase, and the Final Phase) in which students are subjected to varying times in darkness, varying compositions flashed before them, and varying degrees of light and time allowed for drawing. The program has been introduced into the University of Nevada's introductory art curriculum and has been found to teach students to react to any visual array in terms of the monocular cues of position, size, and brightness. [Not available in hard copy or microfiche due to marginal legibility of original document.] (SP)

This study was designed to determine whether a student's level of critical thinking would be increased by exposure to programmed materials which emphasized the use of qualifying words in avoiding over-generalizations. Seventy 8th graders were randomly divided into two groups--one experimental, the other control--which were judged to be equivalent on the basis of scores computed from six pretests--Cornell Thinking Test, Iowa Vocabulary and Reading Subtests, SRA Educational Ability Test, a sentence completion test, and a paragraph composition exercise. The control group used materials dealing with interpreting literature and improving skills in English mechanics while the experimental group used materials focusing on the use of qualifying words in verbal settings. Results of the post-test indicated that (1) the experimental group made significant gains in total number of qualifying words used in sentence completion, (2) the control group made significant gains on mean scores on the critical thinking post-test, and (3) no difference was noted between total number of qualifying words used by the two groups in paragraph composition. Further investigation was recommended to determine the effectiveness of the experimental materials if used over longer periods of time and if presented without paper-pencil restrictions. (Author/JM)

Causal generalizations play a crucial role in educational decision-making: the prospect of discovering the relevant ones motivates much of the support that educational researchers receive and the failure to produce correct and relevant ones motivates much criticism; in this paper my concern is with how we tell when they are correct. (Author/JM)

The intent of this paper is to present a case study in discovery learning using a chronological, narrative history book. (Author)