Large Degree Of Freedom Research Articles

Normal Goodness-of-Fit Tests for Multinomial Models with Large Degrees of Freedom

Normal Goodness-of-Fit Tests for Multinomial Models with Large Degrees of Freedom

Proposition of an Improved Nonparametric Identification Technique for Multi-Degree-of-Freedom Vibratory Systems.

In a previous paper, the authors proposed a nonparametric Identification technique of nonlinear multi-degree-of-freedom systems. Theoretically, the technique can be applied to systems with any number of degrees of freedom, but it has been found that in practical cases the technique is difficult to apply to systems with larger degrees of freedom. The reason is that the unknown parameters for a system become vast as the degrees of freedom of the system become larger. In this paper, an improved technique is proposed which not only requires fewer unknown parameters, but also is more convenient for use in succeeding analysis. Numerical simulation is conducted, and applicability of the improved technique is shown. Furthermore, its advantage in succeeding analysis is demonstrated by applying the identification results to the incremental transfer matrix method.

A finite-element alternating method for two-dimensional mixed-mode crack configurations

A finite-element alternating method (FEAM) is presented for two dimensional mixed-mode cracked problems. An analytical solution is presented for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate. This analytical solution is used as the fundamental solution in the alternating method. For the numerical part of the method the finite-element method is used. For problems of edge cracks emanating from internal boundaries, the method is modified to account for the effect of fictitious crack tip. This modification, the origin-shifting method, is explained in detail. The FEAM is applied to a variety of mixed-mode crack problems with different configurations and loadings to assess the validity of the method. The method gave accurate stress-intensity factors with minimal computing effort. As the method needs to model only the uncracked body, finite-element models with large degrees of freedom are not required and therefore, the method has been implemented on personal computers.

Multifocus processing of L band synthetic aperture radar images of ocean waves obtained during the Tower Ocean Wave and Radar Dependence Experiment

As part of the Tower Ocean Wave and Radar Dependence Experiment (TOWARD) objectives, the mechanisms of SAR imaging of ocean waves are investigated using L band SAR data over the Naval Ocean Systems Center tower. This paper provides experimental evidence needed to validate the differing hypotheses. Various processing methods are investigated to generate spectra with large degrees of freedom. The results show that waves traveling in the aircraft direction are most detectable at focus settings in the range 10.0–15.0 m/s, which is consistent with the Marine Remote Sensing Experiment (MARSEN) observations reported by Jain and Shemdin (1983). Waves traveling in the direction opposite to the aircraft are most detectable at settings equal to −5.0 to −15.0 m/s. The SAR imaging system acts as a low‐pass filter with the peak of the ocean wave height spectrum occurring at higher wave numbers compared with the peak in the SAR image spectrum.

A Recursive Computation Scheme for Multivariate Rational Interpolants

We derive here a recursive computation scheme for the rational interpolation method introduced in [7]. Explicit formulas for these multivariate rational interpolants are repeated in § 2 while the recursive algorithm is described in § 3. A number of interesting special cases such as the univariate rational interpolation problem and the multivariate Padé approximants introduced in [6] and [10] are dealt with in § 4. For some of these rational approximants other recursive schemes were described previously. Finally § 5 contains the numerical results: the multivariate rational interpolants described here are compared with multivariate polynomial interpolants, interpolating branched continued fractions introduced by Cuyt and Verdonk [8], interpolating branched continued fractions introduced by Siemaszko [12] and several multivariate Padé approximants [6], [3], [10]. Besides the fact that our multivariate rational interpolants allow a large degree of freedom in the choice for the numerator and denominator in order to fit the function to be approximated as well as possible, they also produce very accurate numerical results.

Dynamic Response Analysis of Structures with Large Degrees of Freedom by Step-by-step Transfer Matrix Method

Dynamic Response Analysis of Structures with Large Degrees of Freedom by Step-by-step Transfer Matrix Method

Possible orientation of the fatty acid chains in lipopolysaccharide.

The fatty acid chains of the lipid A component of lipopolysaccharides are hexagonally packed with a lattice periodicity of 4.1 A. The smallest subunit of this lattice consists of a disaccharide to which seven fatty acid chains are linked representing the hydrophobic part. Carbohydrates and substituted phosphate residues linked to them form the hydrophilic part of the molecule. Because of sterical reasons and because of the necessity of a separation of hydrophobic and hydrophilic part, we could derive that the angles of the hydrocarbon chains with the planes of the two sugar residues should be as vertical as possible and the planes of both sugar residues should be approximately coplanar forming an angle of about 180 degrees with one another. Conformation angles for all the theoretically possible linkages of the disacoharide and of the linkages of the fatty acid residues have been calculated. Between the two-N-acylglucosamine residues theoretically beta-1,4, alpha-1,6 or beta-1,6 linkages are possible. The experimentally found beta-1,6 linkage has the largest degrees of freedom for its conformation angles.

Simple approximations to the behrens—fisher distribution

Dayal and Dickey (1977) have published in this journal a rather efficient numerical integration procedure for the product of k Student t-densities, and point out the evaluation of Behrens-Fisher (BF) densities as an important special case. The present note adds to this three simple normal approximations to Behrens-Fisher tail probabilities, that will save computer time for someone using the Dayal-Dickey results, and even allow evaluation on a desk calculator for moderately large degrees of freedom. A direct normal approximation (method U) will be too coarse unless both degrees of freedom are large. A combination of the Peizer-Pratt (1968) approximation to the t-distribution and the Patil (1965) t-approximation to the BF distribution turns out to be very accurate. For very small degrees of freedom it may still be refined by an adhoc correction presented below. Other approximations and expansions turn out to be less satisfactory than the present trio. It facilitates a quick evaluation of BF probabilities an...

The small package air freight industry in the United States: A review of the federal express experience

The growth in air freight traffic in the United States can be attributed to the increasing demand for fast and reliable delivery of small and time-sensitive packages. A solution to the problem appears to be an all-cargo airline that can directly operate its own vehicles in a more coordinated fashion and can achieve the economy-of-scale by consolidating traffic. An example can be found in Federal Express—a small package airlines—which provides direct, single source door-to-door service through its own fleet of aircrafts and pickup/delivery trucks. Traffic is bundled up from thin density markets via a concentrated operation in Memphis. These two features in conjunction allow services to be rendered economically to small medium-size cities. The relative youth and entrepreneurship of the airline means that ideas and management techniques are often configured from afresh and executed with diligence. The airline, long qualified as an air taxi, has operated with a large degree of freedom outside the confines of regulatory controls. As the company expands and as a set of national air cargo regulations are evolving, some of the advantage enjoyed by the company may be negated. The future success of the “Federal Express Model” is an interesting case study for both practitioners and researchers in the air freight industry.

Student Goal Centered Learning Program

inaugurated at Burris High School in the 1968-69 school year. The program developed under the concept that students receive greater exposure to the process of learning when they design a series of experiences to reach personal educational objectives based upon individual goals. An individualized pattern of student, teacher, and parent planning was developed which allows students a large degree of freedom along with responsibility. The students themselves are showing the way for a changed curriculum. Learning takes a different form when students work on programs developed from their individual goals. Students who want to know what life is really about work with people of all ages. Teen-agers who have a curiosity about themselves search for understanding. Growth is relevant to living in the larger community rather than the narrow society of the traditional school. Students are exposed to young children and adults instead of the segregated society of their age level. Learning can be exciting and have a great impact on the lives of

Comparison of the sensitivities of similar independent and non-independent experiments

SUMMARY The comparison of sensitivities is considered in detail for a random effects model in which the different methods of measurement are applied to the same experimental units. An exact distribution is obtained and tabulated and approximations to it considered. Other applications of the results are outlined. The problem of comparing two or more methods of measuring the effects of experimental treatments arises in various fields of research. Cochran (1943) discussed this problem in considerable detail under the assumption that analysis of variance techniques were applicable. He suggested that a comparison of the sensitivities of two scales of measurement, or two experimental techniques, should depend both on the magnitudes of treatment effects and the experimental errors associated with the measurement scales, or experimental techniques. A method of measurement for which the differences between treatment effects show up well, and which, at the same time, has a relatively small error variance, will be considered a sensitive method. In this paper we distinguish between three types of situation in experimentation: (i) Type 1. The different methods of measurement are applied to the same experimental units. This can be done whenever not more than one method affects the experimental units. The results of the methods will be correlated. (ii) Type 11. The different methods of measurement are applied to separate subsamples of the same experimental units. Here only the 'treatment effects' for the methods will be correlated. (iii) Type 111. The different methods of measurement are applied to independent experimental units. Schumann & Bradley (1957, 1959) considered the type III situation. Following Cochran's line of thought, they effected a comparison of the sensitivities of two experiments through a comparison of two variance ratios. Their work was restricted to independent experiments and they were mainly concerned with similar experiments in which the variance ratios compared had identical degrees of freedom. They calculated critical values of the ratios of two independent F's to be used in hypothesis tests to compare sensitivities. Schumann & Bradley assumed that analysis of variance techniques were applicable and considered both model I (fixed effects model) and model II (random effects model) of the analysis of variance. Dar (1962) derived a normal approximation to the Schumann & Bradley density function for the ratio of two F's. He showed that the logarithm of the ratio was approximately normally distributed for large degrees of freedom. He also extended the theory to obtain an approximate chi-square test for the comparison of the sensitivities of several

The Relation of Teachers’ Marks to Standardized Tests

Introduction.?Since the early history of formal education there has existed some form of pupil measurement. In recent years the objectives of education have been broadened so that such outcomes as attitudes, habits, and appreciations are considered as impor tant for the proper kind of growth in social experiences as is subject matter or factual knowledge. With the emphasis being placed on these new objectives of education, it is important to know how closely teachers' marks are related to standardized tests of achievement and native ability. Procedure.?The field of inquiry for this study has been limited to the data gathered in the Glenrock-Parkerton School System, Glenrock, Wyoming; The Las Animas County High School System, Branson, Colorado; and the Grover-Hereford School System, Grover, Colorado. The period of testing extended over a period of time beginning with the school year of 1932-33 and ending with the school year of 1936-37. Each of the school systems included in this study was under the direct supervision of the writer. The proce dure was uniform throughout the entire study. There were twenty-three teachers whose marks were included in the study. Of these, fourteen were high school teachers and nine were elementary school teachers. Only two of the entire group of twenty teachers were inexperienced. There was a group of pupils at each of two levels of school work. The first group con sisted of tenth and eleventh year pupils of the senior high schools and the second group was made up of fifth and sixth year pupils of the elementary schools. The tests selected and administered to the high school pupils consisted of the Sones Harry High School Achievement Test and the Otis Group Intelligence Scale. The tests se lected and administered to the elementary school dud?Is were the New Stanford Achieve ment Test and the Otis Group Intelligence Scale. The authors and publishers of these tests claim a high reliability for them. The schools used in the study were what the progressive educationalists would term conservative. However, they were progressive to the extent that teachers were allowed a large degree of freedom in choosing the methods used. The state course of study pro vided the only outline of a curriculum offi cially imposed upon the teachers. Teachers knew early in the year that standardized tests would be administered. However, none of the teachers had access to any standardized tests or their results before they were administered for the purpose of making this study. All of the teachers of high school subjects had standard four year degrees from accred ited colleges. Three of them had earned the Master's degree. Six of them had taken some graduate work in education. All of them had at least twenty-two and one-half quarter hours in education and at least the number of hours in the subject taught equivalent to that termed a minor by many colleges. All of the elementary school teachers had at least two years of college work and three of them had the standard four-year Bach elor's degree. All had majored in education. All those who had less than a four-year de gree had at least twenty-two and one-half quarter hours in education. The Findings.?The average number of cases for the five groups of correlations be tween teachers' marks and achievement, as measured by the Sones-Harry High School Achievement Test, is 128. The coefficients of correlation between teachers' marks and achievement are as follows: language and literature .51; mathematics .36; natural sci ence .18; social science .30; and the average of the above four subjects .54. The average number of cases for the five groups of correlations between teachers' marks and intelligence, as measured by the * Brief summary of: C C Moore, The Relation of Teach ers' Marks to Standardized Tests. Unpublished Doctor's Field Study, Number 1, Colorado State College of Education, Gree dy, Colorado, 1938.