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The author comments on the article "A Simultaneous Equation Approach to Financial Planning." He states that in terms of mathematical connotations, "Simultaneous Equation" is an overstatement and that it is pretentious to call a series of equations "simultaneous" because they are accounting identities. He suggests that the authors should have compared their pro forma model with other models in more details. He states that other pro forma models allow for greater flexibility and have users specify several categories of cost separately a function of variables and fixed values.

Whenever a regression analysis is run, one of the key statistics which is reported is the coefficient of determination or, as it is more commonly known, R[sup 2]. This quantity represents the proportion of the variance of the dependent variable that is associated with ("explained by") the set of independent variables. However, this statistic is a biased estimate of the true coefficient of determination for the underlying population. Moreover, the bias in unadjusted R[sup 2] can be sizeable and may lead to serious misinterpretation of research results. The purpose of this note is to examine the magnitude of the bias in R[sup 2] and to discuss some of the properties of R[sup 2] adjusted for degrees of freedom, a statistic which is less biased than R[sup 2]. The properties of the unadjusted R[sup 2] are examined in the first part of this note. The second part describes the properties of adjusted R[sup 2] when adjustment is considered necessary. [ABSTRACT FROM AUTHOR]

Can analytical models of marketing phenomena be constructed, tested, and understood by persons who are not sophisticated in mathematics? "Yes," say the authors -LOGICAL FLOW MODELS meet the specifications. They are appropriate for the analysis of large classes of marketing behavior. They can yield specific predictions, or be made the basis for computer simulation and sensitivity analysis in much the same manner as their mathematical counterparts. They can be important aids to decision making. [ABSTRACT FROM AUTHOR]

The article discusses the marginal preference model and its applicability in operations research. The article discusses how mathematical models used in operations research are developed and how these models provide measurements that are needed and used to help satisfy human needs. The article discusses measurements, qualitative measurements, and replication. In describing the use of the marginal preference model, the article highlights the preference defined, optimization within constraints, and a test of the model. Discussion of the applicability of the model is also presented.

The article presents the author's view on the usefulness of the computer program "Sketchpad" in business. The author states that Sketchpad can be used to explain mathematics to nonmathematical managers and help them understand how to communicate with computers. The author describes drawing a circle in the Sketchpad application, and the additions that can be made to the drawing using the program. The author uses mathematical equations to illustrate how the computer program works in hopes of making it more understandable for users.

The article discusses the requirement of physics, chemistry, biology and mathematics in the field of oceanography. It was suggested that international cooperation in oceanography is necessary if human understanding of the oceans is to keep pace with human needs. The science of oceanography is an adventure wherein any discipline or combination and using the sea and all that is in it. Oceanography has set a pattern of international cooperation in studying the seas. The kind of survey work necessary to assess all marine sources is one that is to great for any one national and should be done internationally.

The article offers information about the author's comment on the relationship between arts and mathematics. The author holds that the basic affinity between mathematics and arts is psychological and spiritual and not metrical or geometrical. He believes that the first essential bond between mathematics and the arts is found in the fact that discovery in mathematics is not a matter of logic but rather the result of mysterious powers which no one understands, and in which the unconscious recognition of beauty must play an important part. Secondly, the affinity between mathematicians and other artists lies in a psychological necessity under which both labor. Then, the third type of evidence of the affinity of mathematics with arts is found in the comparative history of the arts.

The article presents a discussion about dialectic materialism and modern science. It discusses the conditions in which dialectic materialism creates for scientists and for scientific pursuits. Dialectic materialism holds that internal contradiction are inherent in all things and phenomena of nature, and treats reality being in constant flux and change. The relationship and the contributions of dialectic materialism in physics, theory of relativity, mathematics, and quantum theory are also discussed.

The article outlines the significant contributions of Russian mathematicians throughout history and the leading roles they have always played in the advance of mathematical theory. Among these scientists were Leonard Euler and Nicholas Lobachevsky, discoverer of non-Euclidian geometry. The author contends that Russian mathematics is untainted with any political and socio-economic bias. Most of their mathematicians were active in all fields of mathematical research, specifically applied mathematics. They also liked to publish books and mathematical journals. Nevertheless, they did not have enough freedom in making personal contacts outside Soviet Union.

This paper presents a review of the exact formulae for control limits for P charts and C charts. Also presented are appropriate graphical methods so that these limits may be easily evaluated. The use of the exact methods, given appropriate tables and/or curves, is no more difficult than the approximate methods which are prevalent in the literature. This note is not intended to criticize the approximate techniques which have been used; rather it is intended to illustrate the use of existing theory whereby the errors of approximation may be eliminated. [ABSTRACT FROM AUTHOR]

Optimization is rightly claimed to be the most significant factor distinguishing the modern approach to machining processes from the orthodox one. Practical results can be obtained from the application of mathematical modelling and optimization techniques.
The paper presents a procedure for solution of machining process optimization problems, with the use of theory of graphs and Bellman's optimum principle.
The finite graph G=(N, A) (where N denoted a set of nodes and A the set of arcs) here presents the set of feasible solutions. Each arc represents a corresponding machining operation and each path the feasible machining process.
A number can be associated with each are the increment of criterion for optimality. Using the optimum principle we can find the shortest possible path in the graph, thus solving given problems of choice for the optimal machining process.
There is a variety of ways in which the performance criterion can be formulated. In this paper only those performance measures having sufficient economical justification are considered. We may minimize the costs of machining processes, or optimize economical effectiveness of capital engaged.
The method presented can be applied with every additive criterion, as well as with some non-additive ones. A practical example illustrates the field of possible application of this method. [ABSTRACT FROM AUTHOR]

Exact formulae of a general nature for the calculation of the effective diameter equivalent of flank angle errors for triangular screw threads with rounded roots and crests have been derived. The sign of individual flank angle errors has been taken into consideration, which lead to four possible cases of mating for each threaded element. Thus generalized formulae valid for all the cases of mating of a male or female element are deduced.
Certain simplifications were introduced in the exact analysis which lead to a form more amenable for computation.
Comparison of this latter form with other formulae in current use showed small divergences in the case of Whitworth threads but bigger divergences are expected in the case of threads with steeper flanks. [ABSTRACT FROM AUTHOR]

The article discusses the methods of arithmetic used in accounting with particular focus paid to counting with casters, a visual form of arithmetic. The beginning of the system was associated with using Roman numerals expressed in uniform quantitative units in the Greek abax and the Roman calculus. Accountants practicing manual arithmetic used a board, or flat surface, with lines or squares representing decimal digits, some combination of decimal digits and non-decimal units of currency, weights, and measurements.

The article focuses on the application of mathematical control theory to finance through a model of problems concerning simple dynamic cash balance. It comments on models of time dependent cash balances, solving them through a version of control theory maximum principle. It states that from the point of view of financial analysis, the solutions obtained were intuitively satisfying, and that the simple models needed to be extended to become more realistic and complicated. It suggests that further theoretical research in deterministic and stochastic control theory was required to expand on the models.

The article focuses on the random walk theory of stock price behavior which posits that past stock-price movements cannot be used to predict future market prices that would allow traders to profit from the predictions. If stock price movements were to become predictable enough that a profit were possible, proponents of the random walk theory argue that enough market participants would quickly recognize and exploit the pattern. These market participants compete enough to make all non-random fluctuations so small that they cannot be exploited for a profit. As a result, the trader would be as well off with a buy and hold strategy as he would with a mechanical decision rule based upon past price changes.

The author reports on the place which mathematical training plays in business education. Changes which have occurred regarding the way in which mathematics is taught to business students are discussed. The goals which business schools have regarding the mathematical training of their students are mentioned. Various ways in which knowledge of mathematics is useful in the business world are mentioned, including understanding marketing data, having the ability to create marketing strategies and having the knowledge of how to work with marketing firms. Problems which arise in teaching mathematics are discussed.

The article presents information on different models for motor learning. A model can be a different thing for different persons. For an artist, a model is a person who poses in front of him. For engineers and architects, a model is the final plan of a building. Hence, a model is based on the idea in the mind of a person, and related facts. According to theoretical models of motor learning, learning occurs in a hierarchical manner through different levels of developed habits. Mathematics and computer programming can enhance motor learning. Research by physical educators has been of no significance for the development of learning theory, and physical educators need to do more research on motor learning.