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Articles 6151 - 6159 of 6159

Full-Text Articles in Physical Sciences and Mathematics

Experimental Design Models, J. Leroy Folks Apr 1964

Experimental Design Models, J. Leroy Folks

Journal of the Graduate Research Center

If we were to assume a linear relationship between x and y described by the model y = a + βx + e it is unlikely that we would consider writing the model as y = a + bx + cx + e. It is even more unlikely that we would apply the least squares principle by minimizing Σe2 with respect to a, b, and c. Yet a similar thing happens in experimental design. In fact, it is common practice to use less than full-rank models where the parameters are not defined and, in cases where they are defined, to …

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A Property Of The Mean Stieltjes Integral, J. A. Dyer Apr 1964

A Property Of The Mean Stieltjes Integral, J. A. Dyer

Journal of the Graduate Research Center

The purpose of this note is to consider the following problem. Suppose [a,b] is an interval, f a function in [a,b] and g a function which has a derivative in [a,b].

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On The Estimation Of Parameters When The Observations Are Subject To Measurement Error, Paul D. Minton, Vanamamalai Seshadri Apr 1962

On The Estimation Of Parameters When The Observations Are Subject To Measurement Error, Paul D. Minton, Vanamamalai Seshadri

Journal of the Graduate Research Center

Maximum likelihood estimation of parameters is considered in the situation where a measurement x is taken to mean "x + d." The maximum likelihood estimator for the parameter of the exponential distribution is found for this case and compared with the usual estimator.

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A Geometrically Characterized Reference Frame For The Study Of Cartan Hypersurfaces In N-Dimensional Projective Space, W. Dale Maness Apr 1962

A Geometrically Characterized Reference Frame For The Study Of Cartan Hypersurfaces In N-Dimensional Projective Space, W. Dale Maness

Journal of the Graduate Research Center

In the projective differential geometry of ordinary space a problem of fundamental importance is that of obtaining a covariantly determined reference frame for the definition of local point coordinates and associated power series developments for the equations of curves and surfaces. Much of the celebrated memoir [1] of G. M. Green was devoted to this problem for a surface or 2-dimensional Cartan variety. However, the complete geometric characterization of the reference frame used by Green was not completed until sixteen years later by Bell [2]. In this paper, an extension of Green's "relation R" is given for a linear (n-2)-space …

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A Proof Of A Theorem On Giffin's Paradox, Don E. Edmondson Apr 1962

A Proof Of A Theorem On Giffin's Paradox, Don E. Edmondson

Journal of the Graduate Research Center

For the uninitiated, Giflin's paradox is the name of a condition from economic analysis. One considers a consumer with a certain income faced with the decision of how much of two goods to purchase. Intuitively, one anticipates that this will depend upon the prices to be paid for the goods, and anticipates that if a price is increased the amount purchased by the consumer will decrease ( the other price being constant). If it happens that with an increase in price of a good, the demand for that good increases, then this paradoxical situation is called Giflin's Paradox. The theorem …

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Some Decomposition Theorems For The Vector Space Of Matrix Summability Operators, Ed Kelly Jr., Tetsundo Sekiguchi Apr 1962

Some Decomposition Theorems For The Vector Space Of Matrix Summability Operators, Ed Kelly Jr., Tetsundo Sekiguchi

Journal of the Graduate Research Center

Consider the set T = {(aij) I aij are real } of matrix summability operators on the set B of bounded sequences of real numbers.

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The Estimation Of Parameters In Regression Functions Subject To Certain Restraints, Paul D. Minton, Alfred E. Crofts Jr. Jan 1961

The Estimation Of Parameters In Regression Functions Subject To Certain Restraints, Paul D. Minton, Alfred E. Crofts Jr.

Journal of the Graduate Research Center

We consider two types of problems in maximum likelihood estimation of parameters of linear functions subject to certain restraints. One is a family of lines with equal slopes or intercepts; the other is a pair of lines constrained to meet at a predetermined point. In the case of normally distributed errors with equal variances within each set, the solutions are identical with least squares solutions. In addition to linear functions, non-linear functions which are transformable to linearity may be treated under these methods.

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A Formula For A Class Of Steady State Solutions, Don E. Edmondson Jan 1961

A Formula For A Class Of Steady State Solutions, Don E. Edmondson

Journal of the Graduate Research Center

An integral representation formula is developed to cope with the problem of determining and studying the steady state solutions of a class of differential equations. The class of differential equations studied is y' + yf = g, where f and g are continuous functions admitting period T > 0. The formula then defines a function admitting period T and serves to allow an analysis of the differential equation above. Theorem I delineates some of the properties of the function and Theorem II provides answers to the steady state questions. An application is made to a capacitance circuit problem.

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What Is A Riemmian Manifold?, Frederick Griffin Jan 1952

What Is A Riemmian Manifold?, Frederick Griffin

Journal of the Arkansas Academy of Science

No abstract provided.

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