Search

The article focuses on the plan for the review of mathematics in the eight grade class, which will be taught in November 1902. Prepared by Agnes M. Tuttle, a member of first year pedagogic class, this plan aims to provide mathematical data to be used in the decoration of the classroom. Educational apparatus and materials such as paper, pencil, and plane-table were used. The method used includes several discussions such as talking with children about decorating of the walls of the room, asking them what materials would be needed for work, and measuring of accessible distances, as well as the height of the walls.

The article presents a discussion on the papers written by students of the third grade about the history of the growth of Chicago, Illinois from the time it was a trading post through its pioneer stage. It also presents the first of two sections of the papers entitled "Chicago of Long Ago" and a subject index to provide an idea about the contents of each child's book. It also presents selected sections from the children's works which are most essential in telling a brief story of Chicago's growth through the past century. The papers present correlated works in geography, industrial science, mathematics, handwork, and art.

The paper discusses the predictive ability and the items selected by the Gluecks research organization for their predictive devices are those arrived at by strict analytic multivariate techniques and represent findings that cannot be faulted by criticisms of the Glueck methodology. In 1950, Professor Sheldon Glueck and Dr. Eleanor T. Glueck published "Unraveling Juvenile Delinquency," a multidisciplinary, detailed comparison of 500 delinquent and 500 nondelinquent boys. In 1960, Professor Glueck, at the request of the editors of the "Journal of Criminal Law, Criminology and Police Science," prepared a paper for the issue to commemorate fifty years of publication of that Journal. The first of the criticisms is grounded in the fact that not all individualist used in Unraveling had complete observations on all. 400 items involved in the origin research. The reasons for these missing observations are varied. The nature of missing observations generally decides their impact on an experiment. There are three distinguishable types of missing observations: random, non-random, and indeterminate.

The article defines six criteria, which help assess news story quality readily. Most journalism professors will probably agree that classroom teaching is more fun than paper grading. The reason, perhaps, is that no clear-cut criteria exist for distinguishing the excellent from the good, the good from the mediocre, and the mediocre from the poor story. Mathematics, science and history professors obviously have an easier time-telling right from wrong and strong from weak performance. These different criteria are as, is it accurate?, is it clear?, is it complete?, is it objective?, is it concise? and is it appealing?

In the paper a dynamic structural equation model consisting of a set of difference equations has been constructed in order to examine the process by which groups generate pressures toward uniformity. The model is based on a hypothesis about communication resulting from such pressures. Parameters of the model have been estimated from a consideration of one of the equilibrium conditions of the model. Hypothetical time paths that describe the dynamic behavior of the system have been generated by a series of computer simulation runs. The structural equation model constructed in order to examine the process by which groups generate pressures toward uniformity has led to a number of major insights into this dynamic process. The model suggests that group cohesiveness and the relevance of the issue to the group's functioning produce pressures toward uniformity. Such pressures result in increased pressure to communicate and an increased readiness on the part of group members to change their opinions. Through this process, discrepancy in opinions is reduced resulting in increased group cohesiveness.

The basic difference between what may be called curve fitting and what is here called mathematical modeling is that curve fitting is an ad hoc procedure while modeling focuses on the structure of relationships between variables, If one explains observations by curve fitting there is no reason to think that much more than a convenient summarization of data has occurred. Centroids or Gini coefficients for sets of data do not generally explain but summaries. However, coefficients and curves introduced to summaries data often do not remain as uninterpreted summary measures. Introductory material indicated that the paper was to deal with models that are both realistic enough to be of value in research and simple enough for parameters to be estimated. The authors believe that the models presented meet the realism criteria and believe little would be gained by debate on this in the paper. This indicates a need to examine the models to see what kinds of data are critical in distinguishing between the models and seeing that the considerations which could be said to be involved in designing a critical experiment are built into analysis or built into data collection so that there is discrimination between models where this is considered to be necessary or desirable.

Although there has been much discussion in recent years of the applicability of mathematical methods in the social sciences, little attention has been paid to the interaction of the sociological analysis and the mathematics. In this paper, an example of an extremely fruitful interaction between anthropology and mathematics is described. The interaction has, on the one hand, greatly increased the subtlety and sophistication of the sociological analysis, while on the other hand it has posed interesting mathematical questions. [ABSTRACT FROM AUTHOR]

Let some individuals selected from a population form a subgroup. Let each individual name those individuals whom he considers to be the best members of his subgroup. Based on the number of times an individual was so named, we wish to find the probability that the individual is the best, second best, third best, etc., member of the population. This paper presents a method for the calculation of such probabilities. In so doing, it also offers a solution to the constant frame of reference problem in which individuals from different subgroups must be compared. [ABSTRACT FROM AUTHOR]

With the development of social sciences, intuitive judgement is no longer a reliable means of measurement. Objectivity is one of the essential characteristics of the scientific method. Objective methods of measurement have therefore become necessary. The natural sciences make greater use of the scientific method. Social science data are often qualitative in nature. Convertion of qualitative data into quantitative data involves abstraction of a particular aspect of a phenomenon, neglecting the remaining aspects. Measurement involves mathematics. In order to know the nature of measurement, one ought to grasp the nature and application of numbers. This paper is oriented to the needs of beginners in social research. It brings out in detail various procedures for constructing unidimensional scales, which are indispensable for understanding the recent advancements in procedures like the unfolding technique and multidimensional scaling.

Stochastic relations frequently occur in the social sciences; however, their statistical properties are not well-known. A random relation can be used to model noise or observational error. This paper characterizes the structure of a random relation by deriving the distribution of the structural vector from Q-analysis and by simulating random relations. We propose a measure of structure and apply these concepts to the nominations of esteemed peers by mathematicians. [ABSTRACT FROM AUTHOR]

From the earliest days of research on blockmodeling, one primary goal was to develop a method that would exploit the algebra of the social relations among individuals to describe the social structure of the group. This goal was reluctantly abandoned, however, because the presence of idiosyncratic relational ties in the data obscured the structure and no reliable method for identifying these ties existed. This paper presents such a method. We have found it useful to distinguish emotionally weak ties (Granovetter 1973), those with low intensity, from structurally weak ties, those that fail to conform to the pattern of ties that exist in and are reinforced by the social structure. The latter type of weak ties are the idiosyncratic ties that interfere with attempts to describe a social structure. This paper operationalizes the concept of structurally weak ties and presents an algebraic method for identifying them in sociometric data. This enables us to use the algebra of social relations to identify a blockmodel that describes the social structure of the group. [ABSTRACT FROM AUTHOR]

This paper gives the expression for the number of 2-3 trees, which are known as balanced search trees. Introducing the generating function of 2-3 trees of height h, two expressions of a(h, n) are given, where a(h, n) is the number of n-leaf 2-3 trees of height h. The first is the recursive expression by using Bruno's formula, and the second is the explicit expression by means of binomial coefficients. From the latter expression, an asymptotic formula of a(h, n) is given for the quasi-complete binary trees. [ABSTRACT FROM AUTHOR]

In this paper, we show how to reorder the computations in the SOR algorithm to maintain the same asymptotic rate of convergence as the rowwise ordering and to obtain parallelism at different levels. A parallel program is written to illustrate these ideas and actual machines for implementation of this program are discussed. [ABSTRACT FROM AUTHOR]

Harmonic decomposition is applied to the shallow water equations, thereby creating a system of equations for the amplitude of the various tidal constituents and for the residual motions. The resulting equations are elliptic in nature, are well posed and in practice are shown to be numerically well-behaved. There are a number of strategies for choosing elements; the two extremes are to use a few high-order elements with continuous derivatives, or to use a large number of simpler linear elements. In this paper simple linear elements are used and prove effective. [ABSTRACT FROM AUTHOR]

The Riccati equation arises in various problems, particularly in practical engineering problems. It is required to solve the resulting Riccati algebraic matrix equation instead of solving the time-invariant optimal control problem in one of its standard forms. In this paper an unconstrained minimization technique referred to as the Davidon-Fletcher-Powell (DFP) method is used in solving such an equation by minimizing its norm. The positive-definite solution of the equation is also obtained, which is desirable in most engineering problems. [ABSTRACT FROM AUTHOR]

The class of indexed languages properly includes the class of context-f ret languages and is properly included in the class of context-dependent languages [1]. The emptiness problem (the problem of determining whether or not the given language is empty) is polynomial-time complete for the class of context-free languages and is undecidable for the class of context-dependent languages. The recognition problem (the problem, given a language L and word W, of determining whether or not W belongs to L) is polynomial-time complete for the class of context-free languages and is polynomial-space complete for the class of context-dependent languages. This paper shows that both the emptiness and recognition problems are exponential-time complete for the class of indexed languages. It is known in the pebble game [2] that the problem of determining whether or not the first player baa the winning strategy is exponential-time complete. This paper reduces the problem to the emptiness problem for the class of indexed languages in the logarithmic space, indicating the exponential-time difficulty of the emptiness problem for the indexed language. Since Also has shown that the problem can be answered in exponential time, the exponential-time completeness is shown. The exponential-tine difficulty is also directly indicated from the fact that the emptiness problem is exponential-time complete. Consequently, the recognition probe tern is also exponential-time complete. [ABSTRACT FROM AUTHOR]

Recently. a new class of error indicators and estimators for the finite element method has been introduced which is particularly easy to implement into existing finite element codes. This paper proves that the new indicators are equivalent to those analyzed earlier by Babuska, thus showing that the rigorous mathematical results for the well-known jump indicator apply also for the new ones. [ABSTRACT FROM AUTHOR]

This paper proposes a highly efficient coding method suited to the storage and transmission of complicated line drawings such as topographical map. Instead of using the method based on the fixed-length segment such as Freeman's chain code, the segment length is made variable according to the state of the curve. The high efficiency is realized by further adding the directional- difference code. in the method employing variable-length segment, there is a danger that the approximate error is increased with the length of the segment. Consequently, a scheme is employed in which the permissible error is specified, and the coding is performed within the error limit. To simplify the encoding procedure, several quantization templates are prepared with different segment lengths, and the approximating segment is selected by taking the template according to the state of the curve. Avoiding the increase of coding complexity by adding the template discrimination code the template to be used is selected based on the code sequence generated in the past. By this scheme, although depending on the complexity of the line drawing, the coding complexity can be reduced by 25 to 40 percent considering only the effect of variable segment length. [ABSTRACT FROM AUTHOR]

This paper presents a simple algorithm for verifying the non-singularity of parametric transformations with quadratic Jacobian determinants. The method is suitable for such transformations applied to all convex polygonal two-dimensional master-elements, but emphasis is placed on the triangle and the square. Geometric insight is used to curtail testing procedures where possible. The algorithm is compared for efficiency to a related procedure in which no use is made of the geometry of the implied curves. Results indicate that the geometric procedure, while slower in some cases owing to additional tests, is considerably more efficient for those cases where the geometry allows early termination of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper is shown the effect of plate thickness on the spectral properties of the stiffness matrix which is obtained from finite element representation. The results confirm the very stiff properties associated with the strata energy based on Reissner and Mindlin theories in the case of thin plates. On the other hand, the Bergan and Wang approach converges to exactly the classical thin plate solution as the thickness decreases. [ABSTRACT FROM AUTHOR]