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SUMMARY CAE has enabled vibrational problems, which were regarded as intractable 20 years ago, to be solvable by students using computational support. The paper describes a problem set to final year undergraduates which concerns the torsional vibrational response of a three degrees of freedom system which is subjected simultaneously to three different arbitrarily varying torques. The solution involves the use of standard library routines for matrix multiplication and eigensolutions, a Runge-Kutta routine to solve a second order differential equation and general competence in writing software.

The man trying to find a fault may make mistakes unless he asks effective diagnostic questions and verifies the answers. General principles for verifying indications in petroleum refineries are presented; some are easy to apply, others require instruction, practice or experience. Simple scores for verification or checking, C, and for effective diagnostic questioning, D, are proposed and their calculation is illustrated in the context of fault-finding in a crude distillation unit. C and D probably measure different fault-finding skills. The C score is improved by training, but comparisons are complicated by an apparent influence of the proportion of instrument faults in the problem set. Men may check instrument readings more often as their estimate of instrument unreliability increases. The D score is also sensitive to the effects of training and reflects differences in experience between novices and experienced men. D may over-estimate effective diagnostic strategy, but only in a small percentage of cases for men with refinery operating experience or new entrants after training.

This paper is concerned with a vector optimization problem set in a normed space where optimality is defined through a convex cone. The vector problem can be solved using a parametrized scalar problem. Under some convexity assumptions, it is shown that dependence of optimal solutions on the parameter is Lipschitz continuous. Hence differentiable dependence on the solutions on the parameter is derived.

This study examined the relationships between the Myers-Briggs Type Indicator Sensing-Intuition and Thinking-Feeling scales, and the choice of autocratic versus participative decision-making methods as measured by the Vroom/Yetton Problem Set. Data from 62 graduate business students indicate that sensing types tend to be more participative than intuitive types. Further analyses suggest that situational factors may be more important than individual differences in influencing the choice of autocratic versus participative decision-making methods.

This paper presents a new method for health problem assessment, called IMP. It is based upon the premise that the critical step in the development of policy decisions isthe definition of health problems at the community level. The method is an extension of the Delphi technique but has been significantly improved by the determination of the critical variables in the problem set and by the incroporation of a structured logic system and of professional judgment. The study compares the IMP method with data gathered by traditional, epidemiological prevalence surveys and also with data from a computer simulation. The conclusion is unavoidable: the IMP method is an accurate as the other methods, at far less cost. The problem of preventable bureaucratic blindness has been used as an illustration of the application of this technique.

In this paper, computational results are reported for Gass' Dualplex Method which is designed to solve dual angular structured linear programs. The test problem set includes a group of staircase problems from such diverse areas as economic development, agricultural planning, and cutting stock models. Each test problem is solved by an experimental dualplex code and an efficient commercial version of the simplex algorithm for comparative purposes. Based on the test problem results, the dualplex method is found to exhibit very good solution behavior and have steeper solution convergence than the commercial simplex code.

For both engineering physics and life science physics sequences, machine‐graded problem sets derived from textbook problems drastically reduce the grading time while substantially increasing the student effort outside of class. With simple modifications, the problem sets can be reused each time a course is offered. Such problem set grading has some of the merits of computer‐assisted instruction, but is considerably lower in cost and applicable to large classes and students who have little time on campus.

Summary Thirty-seven graduate students in nursing were given the problem set, used by Tversky and Kahneman in their study on the “law of small numbers,” as an extra credit part of a final examination for a statistics course. While some conservativism was noted, the major Tversky and Kahneman postulates were supported. These incidentally obtained replication data provide support for the contention that the tendency, induced by representativeness, to confidently make inferences is only slightly, if at all, determined by factors such as statistical and empirical sophistication, availability of normative criteria, knowledge about the shortcomings of human judgment, and the conditions under which inferences are to be made.

We have shown that it is possible to account for a substantial portion of variability in student responses to arithmetic word problems using variables that describe structural features of the problems. However, the results obtained at this stage in our investigations are situation-dependent. The greater variance in observed proportion correct compared with the variance in the predicted proportions, and the differing sets of variables contributing significantly to the regressions come as no surprise. First, the population for this study differed from that used in the pilot study. Second, it is clear that characteristics of the problem set, for example, the frequency of occurrence of exemplars for the range of values for each variable and the way variable values are combined in problem types, affect the weighting for each variable in the regression analysis. Thus, differences were expected because different problem sets were used for the pilot study and the present study. In the light of these differences, the similarity in performance of the two disadvantaged groups gains in significance, and deserves further study. We believe we can increase the generalizability of our results by redesigning the basic problem set to exemplify in a balanced fashion the full range of variables found to account for problem difficulty. Given, however, the difficulty of making accurate predictions about problem-solving results, the correctness of this belief needs to be explicitly tested.

This article deals with classroom application of cognitive psychology. It reviews briefly some of the research related to the development of automaticity for recall of basic math facts, reports on a single-subject research project, and gives teaching suggestions for the development of automaticity. The research project reports on six students in fourth and fifth grade who were presented addition problems on a computer for 5 minutes daily over a period of at least 27 days. Using an ABAB design, all students were exposed to large and small sets of problems. Student response time, measured as initial keystroke latency on the computer, decreased dramatically as did time needed to complete written posttests. An analysis of the effects of practice set size revealed no differences when practice sets contained only 3 new problems out of 10 on a large problem set of 20 problems.

The two objectives of this paper are 1) to give a large and varied problem set, complete clause sets for use in testing automated theorem-proving programs and 2) the presentation of a number of experiments with an existing program under a variety of conditions.

A proposed standard set of test problems is described and applied to representative quadrilateral plate and solid brick finite elements. The problem set contains patch tests and beam, plate, and shell problems, some of which have become de facto standards for comparing the accuracy of finite elements. Although few in number, the tests are able to display most of the parameters which affect finite element accuracy.

Alternative courses which present themselves when a new university is being planned are to replicate a traditional model, or to explore new ways of promoting scholarship, drawing on the experience of existing universities and their staffs and students, and on perceptions of external needs and pressures for various sorts of learning. The latter course was followed by Griffith University, Brisbane, which opened in 1975. The decision to organize academic activities in non‐departmental schools, each with a unifying theme or problem set orientation, in combination with concern at the cumbersome decision making processes of more traditional forms, led to the design of a relatively decentralized policy making and executive structure: a Council, supported by a range of policy making and advisory committees each with explicit responsibilities and authorities; a limit number of academic and other operating divisions, each headed by an executive officer with substantial delegated authority; and a structure for an emphasis on horizontal interaction.

The author's inquiry [1] on learning systems is generalized in the following respects: The process of learning, instead of coming to an end when the learning goal has been reached, is supposed to last for ever, so that the above "definitive" learning as well as phenomena such as forgetting, re-learning, changing the goal etc. become describable. We take over the notion of semi-uniform solvability of a set Γ of learning problems (2.2), but now (trivial cases excluded) the whole capacity of a learning system is never s. u. solvable. Finite such sets Γ are. The notion of a solving-basis of some Γ is introduced and we can state necessary conditions that Γ possess such a basis (2.14), so that examples of sets Γ without a basis can be provided. On the other hand, any s. u. solvable Γ has as basis. The notion of uniform solvability (3.1) reinforces that of s. u. solvability, and there are given sufficient conditions for Γ to be uniformly solvable (3.6). In some "finite cases", s. u. solvability, existence of a basis and uniform solvability coincide (3.7---3.9). At last we give the construction for the weakest learning system solving a uniformly solvable problem set (3.12---3.19).

[EDITORIAL NOTE.-The editors of this Journal are the officers of the Elementary School of the University of Chicago. They present with very great satisfaction the following article as a full, concrete illustration of the application of impersonal scientific methods to elementary-school problems. In the near future other studies of larger school systems will be presented, and it is hoped that the significance of this method will be widely recognized. If studies of this type could be made in every school system, supervision and administration of schools would rise to a level never attained in any educational system. Attention is not unlikely to be drawn to those parts of the report which seem to show defects in the work of the University Elementary School. In later years similar reports will be made, and it is hoped that concrete evidence can then be presented of the advantages of knowing one's own weaker points. This study is the basis of the present administration of the school. The officers of the school are clear also that their problem is not merely to prepare for high school. The Elementary School does many types of work not touched on in this report. The aim of the school, however, is to do the conventional types of work in such a way as to achieve equal efficiency with other schools and at the same time to work out problems not taken up by these other schools. Finally, the significance of these results will not be fully appreciated by any reader who fails to recognize that the high school is studied by these tables quite as much as the elementary school. Is the relation here discovered in history due to the training in the elementary school or to the methods employed in the high school? The practical answer to this question is to be found in the fact that the history instructors in these two schools have been organized since the preparation of these tables into a single department. They have their problem set before them in impersonal and yet very emphatic form.-THE EDITORS.]

In the recent literature, a paper1 and a contract report2 indicate that automatic analog computer patching sys tems have become economically and technologically feasible. In anticipation of the development of a variety of proposed patching systems, a specific decision pro cedure is developed for the rational evaluation of com peting automatic analog patching systems. The design procedure described in this paper facilitates selection of the patching system best suited for a partic ular computer and a particular problem class. Sufficient information is abstracted from a typical problem set to determine the number of relays required for (and thus to assign a cost figure to) each possible patching system without requiring the actual design of each system. Nom inally, the best system is that with the lowest cost figure. It is recognized, however, that there are many subjective decisions (e.g., captive vs. free pots) involved in the de sign process that are not quantified in this overall cost figure. This problem is met in part by providing inter mediate information relating to the optimal module size, combinations of proposed systems, etc. to help estab lish some of the sensitivity properties of the optimal system. The procedure is illustrated by applying it to a particu lar case and evaluating a number of alternative switching systems.

The manufacturing technology of the 1980s in the chemical and petrochemical industry is not likely to show any radical change. There will, however, be significant advances in some general areas. Part I of the paper is concerned with developments arising from exploitation of fundamental research in the molecular sciences and in biochemistry and microbiology. These are expected to lead, respectively, to methods for the design of selective catalyst and improvements in separation processes, and to increasing use of biochemical processes. Part II discusses developments in operation and design, aim ed at reducing construction and operating costs; particularly to make best use of materials and energy, and to conserve the environment economically. In all areas the pace of technological development will depend on the ability of industrial teams to exploit the results of fundamental research. Both research and the development stemming from it will continue to be dependent on increasingly powerful measuring and computing facilities, as also will be the larger and more closely integrated production complexes. The scientist and the engineer welcome the aid of the computer to extend their own abilities, b u t others (such as process operators) fear their introduction will take away the interest of their work an d ultimately eliminate their jobs. This will pose a serious problem to m anagement, not only on the plant, b u t in all departments of a company. Careful planning and experiments will be essential to ensure th at all personnel have satisfying jobs and can develop their full potential. This is one aspect of the much wider problem set by the need of all organizations (industrial, political and social) to improve the design of their structure and management, to meet the individual’s legitimate aspirations in a changing society. It is suggested th a t the application of the concepts o f system analysis and control engineering will contribute significantly to the solution of this problem : but the major contribution must come from sociology and the hum an sciences.

The focus of this study is to investigate low and high spatial ability students’ potential creativity in geometry. Students were member of Anatolian and State High Schools, in Marmara region of Turkey. Purdue spatial ability, a likert scale instrument (PISA, 2003) and geometry problem set have been used to collect the data. Findings showed that students in state schools have low spatial ability levels than the Anatolian Students. Furthermore, Anatolian students and State School creativity levels were not different with easy geometry problems.

This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our meeting was to bring together researchers from a variety of disciplines, with a common goal of understanding different viewpoints and approaches surrounding the theory of mathematical quasicrystals. The problems below reflect this goal and this diversity and we hope that they will motivate further cross-disciplinary research and lead to new advances in our overall vision of this rapidly developing field.

The increasing appearance of an integrated statistics and research design course is noted, and the use of computer simulation in such a course is discussed. Four different kinds of courses are suggested: the problem set course, the demonstration labs course, the design-your-own course, and the “research community” course. Example simulations are discussed for each course.

The present work gives a brief comparison of the performance of programs for integrating differential equations for orbital applications. The evaluation criteria and the method of testing are described, and the results of the test problem set are included. Integration methods that were chosen for comparison include high-order Runge-Kutta methods; a rational extrapolation method (Bulirsch and Stoer, 1966); a variable step, variable order, multistep method (Krogh, 1969); classical multistep methods of Adams and Cowell; and modified multistep methods. The high-order Runge-Kutta methods used in the comparison include RKF 7(8) and RKF 8(9) (Fehlberg, 1968), and RKS 8-10 (Shanks, 1966).

Publisher Summary This chapter discusses the convergence of the reduced gradient method. The reduced gradient method includes operations similar to those of the simplex method, with additional operations resulting from the nonlinearity of the objective function. The chapter describes a variant of the reduced gradient method, providing a sequence, generally infinite, of feasible solutions whose accumulation points are optimal solutions of the problem posed. In the case of a linear objective function, the proposed algorithm is considerably simplified and converges in a finite number of iterations. The chapter describes how a classical polynomial disturbance of the second member of the constraints transforms the problem set into a neighboring problem that verifies the non-degeneracy hypothesis.

A Problem Solving Environment (PSE) is an integrated system of application tools that support the solution of a given problem, or a set of related problems. Paramount in the development of such environments is the design, specification and integration of user interface tools that communicate between the application tools of the system and the user. Typically these interactions are object oriented and involve the interaction with tool parameters, which in many applications (CAD/CAM, Imaging Systems, Image Processing), are represented by graphical data. This paper describes a user-interface tool development system in which both textual and graphical display, and interaction techniques are integrated under a single model. This allows the user to interact with tool parameters in either graphical or textual modes, and to have the parameters displayed in the manner most relevant to the problem set.

A study was conducted to define a Multimode CPU architecture in which the CPU could handle instruction addressing, data addressing, and data processing. A problem set of signal processing tasks was defined from which the architectural design evolved. The multiplier/FFT interaction was identified as a major architectural constraint. A RALU structure was defined to perform the data addressing and data processing. A microsequence structure was designed to perform the instruction addressing. Two complex-data signal processors were defined and designed at the register level. These processors, along with the Raytheon Micro Signal Processor and the Tracor/RCA General Processing Unit were addressed on their ability to perform benchmarks from the initial problem set. (Author)

The essential features of the reservoir codes CHARGR and MUSHRM are described. Solutions obtained for the problem set posed by DOE are presented. CHARGR was used for all six problems; MUSHRM was used for one. These problems are: the 1-D Avdonin solution, the 1-D well test analysis, 2-D flow to a well in fracture/block media, expanding two-phase system with drainage, flow in a 2-D areal reservoir, and flow in a 3-D reservoir. Results for the last problem using both codes are compared. (MHR)

Decision-theoretical critique of ‘semantic information’ measures and of some other suggestions made by students of inductive logic leads to a formal statement of the following sequence of the scientist’s choices: (1) ‘What Problem shall I study?’ — chosing one of the sets of states of Nature ‘payoff-relevant’ to the scientist. (2) ‘What set of mutually exclusive and exhaustive Hypotheses shall I test?’ — chosing a partition of the Problem set. (3) ‘What kind of Evidence shall I use?’ — chosing a set of observations presumably related statistically to the set of Hypotheses. (4) ‘What Rule for accepting a hypothesis shall I use?’. (For a certain class of the scientist’s payoff functions, the Rule is to accept a hypothesis with maximal posterior probability.) To be optimal the four choices must be made simultaneously and will depend on the payoff functions for the alternative Problems, on the initial probabilities of states of Nature, and on the costs of testing, computing, storing and communicating (the latter costs are related to ‘teachability’ or ‘simplicity’).

The scripts generated in written interactive communications between users and a computer consultant program were investigated in a controlled experiment. The program was a simulation of UC, the UNIX Consultant, which users believed to be the actual program. An analysis of the scripts generated while solving a predefined set of problems showed the heavy use of context in forms such as ellipsis, anaphora, indirect speech acts, and grammatically incomplete sentences in over one-quarter of input clauses. Also present were grammatically ill-formed constructions and spelling errors. A comparison with a control group of users solving the same problem set with human consultants showed that the control group relied on context about twice as much as the simulation group. This suggests that people naturally use context in language and that the simulation group tried to rely less on context because they believed that they were speaking to a computer. Even so, contextual information is essential to understanding a large part of the simulation group's input.

The objective of this work was to perform an assessment of prediction capabilities and features of the PORFLO code in relation to its intended use in the Basalt Waste Isolation Project. This objective was to be accomplished through a code verification and benchmarking task. Results were to be documented which either support correctness of prediction capabilities or identify areas of intended application in which the code exhibits weaknesses. A test problem set consisting of 10 problems was developed. Results of PORFLO simulations of these problems were provided for use in this work. The 10 problems were designed to test the three basic computational capabilities or categories of the code. Broken down by physical process, these are heat transfer, fluid flow, and radionuclide transport. Two verification problems were included within each of these categories. They were problems designed to test basic features of PORFLO for which analytical solutions are available for use as a known comparison basis. Hence they are referred to as verification problems. Of the remaining four problems, one repository scale problem representative of intended PORFLO use within BWIP was included in each of the three basic capabilities categories. The remaining problem was a case specifically designed to testmore » features of decay and retardation in radionuclide transport. These four problems are referred to as benchmarking problems, because results computed with an additional computer code were used as a basis for comparison. 38 figures.« less

A statistical analysis of the solution times of the algorithms in the Sandgren-Ragsdell study is conducted. An analysis of variance is performed to demonstrate that there is statistical evidence that selected codes are superior to others on the basis of their relative solution times. A logarithmic transformation is used to produce a seminormal distribution of the solution times with a variance assumed to be equal for all of the algorithms. A paired comparison is then conducted on the differences in the mean logarithmic solution times for each of the algorithms over the entire test problem set. The selected confidence level for all comparisons was fixed at 95%. The factors contributing to the success of this analysis are discussed as well as the additional data which would be required to conduct this type of analysis in general.

The results of numerical experimentation designed to test some existing routines (Newton, Secant, Brown, Powell, Broyden, and others) for solving nonlinear systems of equations are reported. The design of the testing procedure as well as the characteristics of the testing problem set are described. The methods are compared with respect to several efficiency measures and domains of convergence. Depending on the characteristics exhibited by a given nonlinear system, an indication is given as to which method is best suited for solving the given problem.

The purpose of this document is to present in organized fashion the necessary tools, excluding textual material, for a 4-week course in Q-7 coding. Because of the nature of the material, each volume is published separately. They are as follows: TM-1118/001/00 - Introduction; TM-1118/002/00 - Outline/ Bibliography; TM-1118/003/00 - Problem Set; TM-1118/004/00 Problem Solutions; TM-1118/005/00 - Examinations, P.A.T.s (Programming Aptitude Tests); and TM- 1118/006/00 - Class Problem. Volumes 2, 3, and 6 can be given to the students along with the documents listed in the bibliography. Volumes 4 and 5 must obviously be restricted, and are published in limited form. The course as out lined in Volume 2 has been classroom tested, and the order of presentation has proven to be satisfactory. Specific areas may be modified to suit individual tastes without altering the course as a whole. Discretion must be exercised in doing so, however, because the problem sets and exams presuppose use of the outlined chronology.

THE Pythagorean theorem says something about area that many students do not notice: given any two squares with areas a2 and 62, it is possible to construct a single square of area c2 that is equal to the sum of a2 and b2. This construction is, of course, usually done by using a right-angle triangle. However, there are cut-and-paste methods that do not use a right triangle directly, but rather cut two smaller squares into polygons that can be reassembled to form the larger square, c2. By "discovering" the decomposition and the reassembly method, the student makes vivid for himself the area relationship stated in the Pythagorean theorem. There are many different ways to decompose the two squares; one standard decomposition is suggested here, with the two smaller squares cut into at most seven pieces. The problem may be posed in non mathematical terms as the construction of a two-way jigsaw puzzle, and as such can be used as an enrichment activity for students of various ages and abilities. The problem set below has proven to be an interesting homework exercise for college students in a liberal arts math course, as well as for future junior high and secondary teachers in a geometry course.

Four squirrel monkeys were tested on a series of five learning problems. The first three problems involved the discrimination of two stimuli while each of the last two problems consisted of 10 stimuli divided into two response classes. Analysis of the proportion of correct responses to individual stimuli within a problem set revealed strong position-habit errors and suggested that S does not learn the correct response to all stimuli of the same problem set with equal facility. This differential level of responding was more pronounced for the 10-stimulus problems than for the 2-stimulus problems.

Structure solution skills in x-ray crystallography are critical capabilities for students and postdoctoral trainees in biophysics, biochemistry and structural biology. While many institutions have incorporated classes on theoretical crystallography into their curricula, practical structure solution skills are rarely imparted through coursework.We thus developed an enabling, hands-on crystallography sub-curriculum, which can be added to existing biophysics curricula that focus on the theoretical foundations. Taking place in an encouraging, collaborative learning environment, our educational intervention sets out to provide learners from diverse backgrounds with sustainable skills to tackle real-world, protein structure solution problems independently.Our curriculum is designed in a multimedia-enhanced, blended classroom format: Reading resources as well as short, narrated and pre-recorded slide presentations provide course participants ahead of class with the necessary background to work on problem sets during face-to-face sessions. Part of an evolving case study, the problem sets contain real-world diffraction datasets in various degrees of difficulty. Throughout the curriculum, learners are sequentially guided through all essential structure solution steps, from remote diffraction data collection and processing, various structure solution strategies, to structure quality evaluation. By the end of the curriculum, every student shares their experiences in an audio-supported slide-presentation over the web, while classmates provide feedback.We evaluate learners' confidence, academic performance and sustained skill level through a multi-facetted set of assessments, including quizzes, problem set solutions, final presentations, peer feedback, pre- and post course surveys, as well as a comprehensive structure solution set to be solved in a longterm post-test. Participants showed good problem solving- and very good crystallographic communication and feedback skills. Their confidence level applying x-ray crystallography techniques increased during the course. Most importantly, three months after the course, >80% of participants were able to solve and refine unknown diffraction datasets to publication quality level.

The effects of the certainty of individuals' self-perceptions on their related self-presentations were investigated. Subjects were given either a problem set which would ostensibly predict their future performance or sample problems which would not afford an accurate prediction. They also received fictitious success or failure feedback on their performances. Self-presentations were measured by having subjects select 20 problems to solve from tests which varied in difficulty and in how well they could diagnose high and low task ability. Subjects believed that their choice of problems and scores would be known to other group members. When subjects believed that prior performance would accurately predict future performance, self-presentations were consistent with subjects' self-perceptions. However, under low certainty conditions, self-presentations were uniformly positive and unaffected by prior performances. The results appear to support the hypothesis that self-enhancement motives are of sufficient strength to occasion risk-taking in self-presentations when subjects believe they have a chance of succeeding.

Presentation of a question that would be suitable for a take-home exam or a problem set in a general or analytical chemistry course.

attempt to test this hypothesis involved the tape recording in the adjoining room. Subjects were asked to fill out a multiple-choice test based on the content of that recording. The problem set by the test was one of correct recognition of the material reproduced from the tape. Analysis of the data gives no indication of a difference between A and D groups in the recall of this material. The within-group variation is great, as is that between groups, in each of the experimental variations.