The Factorisation of the rectangular distribution

1967 ◽  
Vol 4 (3) ◽  
pp. 529-542 ◽  
Author(s):  
T. Lewis
Keyword(s):  
Bounded Variation ◽  
Distribution Functions ◽  
Absolutely Continuous ◽  
Rectangular Distribution ◽  
Factor Type

Questions of the decomposability of distribution functions into real-valued components of bounded variation were discussed by P. Lévy (1964) in relation to the nature of the components, whether non-decreasing (distribution functions in particular) or absolutely continuous (a.c.) or both. Hanson (1965), in a review of Lévy's paper, raised the question of whether or not a rectangular distribution could be decomposed into two a.c. distributions. In fact, D. G. Kendall had conjectured earlier (Kendall (1960)) that no such decomposition is possible. The object of this paper is to state and prove the truth of Kendall's conjecture. “Decomposition” or “factorisation” will be understood throughout the paper to mean decomposition into distributions. Decompositions of the rectangular distribution into one a.c. and one discrete factor are well known (see, e.g., Lukacs (1960) pp. 128–9), and decompositions in which both factors are singular continuous (s.c.) have been discovered by Kendall and by P. M. Lee; it is shown here that no other combinations of factor-type can exist. References to other work on related decomposability properties are given in the papers by Lévy and Kendall cited above.

Birth Dates and Death Dates: An Examination of two Baseline Procedures and Age at Time of Death

1990 ◽  
Vol 20 (2) ◽  
pp. 127-137 ◽  
Author(s):  
Albert A. Harrison ◽  
Neal E. A. Kroll
Keyword(s):  
Young Men ◽  
The Other ◽  
Birth Date ◽  
Time Of Death ◽  
Low Frequencies ◽  
Temporal Proximity ◽  
Rectangular Distribution ◽  
Old Men ◽  
Day By Day ◽  
Death Date

The present study continues analyses of variations in the frequencies of death in the near temporal proximity of decedents' birthdays. Observed frequencies were compared with expected frequencies as ascertained from two baseline distributions. One distribution was the usual rectangular distribution, based on summing the number of deaths across all frequency categories and then dividing by the number of categories. The other distribution was constructed by pairing one person's birth date with another person's death date. This latter distribution was intended to provide a true baseline, and provide a better gauge for assessing the likelihood that any obtained relationship reflected coincidence or chance. Two weeks before and two weeks after the birthday there were more deaths, and one week after the birthday there were fewer deaths, than would be expected on the basis of either baseline distribution. Day-by-day analyses within the birthweek confirmed earlier reports of high followed by low frequencies of death. Compared to relatively old men, relatively young men were more likely to die on the eve of their birthdays or on their birthdays themselves. Compared to relatively young men, relatively old men's death dip begins at an earlier point in time. Methodological and theoretical implications are discussed.

An Experimental Investigation of Temperatures in Grinding of Ceramics with a Brazed Diamond Tool

2014 ◽  
Vol 1027 ◽  
pp. 8-11 ◽  
Author(s):  
Xin Xiang ◽  
Jiang Quan Wang ◽  
Jian Yun Shen ◽  
Xi Peng Xu
Keyword(s):  
Diamond Tool ◽  
Measured Temperature ◽  
Moving Heat Source ◽  
Energy Partition ◽  
Matching Method ◽  
Workpiece Surface ◽  
Rectangular Distribution ◽  
Grinding Tool ◽  
Good Relation ◽  
Temperature Responses

An investigation is reported of the relationships of the temperatures and grinding parameter for grinding of ceramics with a brazed diamond grinding tool. During the experiments, the temperature distributions along the workpiece surface were measured using a foil thermocouples and the energy partition to the workpiece estimated using a temperature matching method. The results show that the grinding temperature increased with the increasing of worktable feed rate or tool velocity and depth of grinding. The measured temperature responses were found to be in good relation with the analytical results of a moving heat source with a rectangular distribution at the grinding zone.The energy partition ε is about 23%.

scholarly journals CO in the Bipolar Nebula NGC 2346

1989 ◽  
Vol 131 ◽  
pp. 205-205
Author(s):  
A. P. Healy ◽  
P. J. Huggins
Keyword(s):  
Planetary Nebula ◽  
Molecular Form ◽  
Central Star ◽  
Minor Axis ◽  
Molecular Gas ◽  
Astronomy Observatory ◽  
Star System ◽  
Mapping Data ◽  
North West ◽  
Rectangular Distribution

We report on observations of the J = 2-1 line of CO to study the distribution and kinematics of the molecular gas in the bipolar planetary nebula NGC 2346. The data were obtained with the National Radio Astronomy Observatory 12-m telescope whose beamsize (FWHM = 30″) partially resolves the CO emitting region. A map of the velocity integrated emission shows a roughly rectangular distribution, approximately 53″ × 34″, oriented along the minor axis of the optical nebula. The CO spectrum towards the central star system is strongly double peaked. The mapping data show that this results from two distinct regions which are offset south-east and north-west of the center with radial velocities which are, respectively, larger and smaller than that of the star system. Overall the CO data are consistent with an expanding and partially disrupted distribution of molecular gas around the waist of the optical nebula. Mass estimates confirm that a substantial amount of the matter ejected by the star system is still in molecular form.

Simulation of Ceramic Injection Molding for Zirconia Optical Ferrule

2007 ◽  
Vol 336-338 ◽  
pp. 997-1000 ◽  
Author(s):  
Mei Min Zhang ◽  
Bin Lin
Keyword(s):  
Injection Molding ◽  
Injection Molding Process ◽  
Molding Process ◽  
Melt Temperature ◽  
Ceramic Injection Molding ◽  
Rectangular Distribution ◽  
Simulation Results ◽  
Die Temperature ◽  
Ram Speed ◽  
Short Shot

Zirconia Ferrule is a key part for manufacturing fiber connectors. The ceramic injection molding (CIM) process of the optical ferrule was simulated with the commercial CAE software moldflow. In order to obtain the optimum results, the orthogonal method was introduced to discuss the influence of each parameter such as die temperature, melt temperature, ram speed and gate dimension with the two kinds of distribution layout system respectively. The simulation results show that the curved distribution runner system is more suitable than the rectangular distribution one in the optical ferrule molding. Moreover, the effect of gravity on the ceramic injection molding process was discussed for determining a more reasonable balanced runner system of the special designed two-plate mold with six die cavities. It was found that short shot occurred at the top of the die cavity while other five cavities were filled well in the original designed mold. And when the top die cavity’s round runner with section diameter of 4.0mm was increased to 4.17 mm, each cavity was balanced filled without short shot.

Effects of a Timing Signal on Simple Reaction Time with a Rectangular Distribution of Foreperiods

1973 ◽  
Vol 25 (3) ◽  
pp. 344-353 ◽  
Author(s):  
Jean Requin ◽  
Marilyn Granjon ◽  
Henri Durup ◽  
Guy Reynard
Keyword(s):  
Reaction Time ◽  
Simple Reaction Time ◽  
Time Course ◽  
Estimation Error ◽  
Time Estimation ◽  
Main Hypothesis ◽  
Frequency Distributions ◽  
Simple Reaction ◽  
Rectangular Distribution ◽  
Simple Rt

It was hypothesized that the time course of preparation during a variable interstimulus interval (ISI) of a simple reaction time (RT) experiment was partly determined by the subjective distribution of conditional probabilities of the executive signal (ES). Sixty subjects performed a simple auditory RT task with various ranges of six ISI durations organized in rectangular frequency distributions. In order to give the subjects information about elapsed time during ISI, a recurring time-marking click, the periodicity of which was varied, was introduced during the ISI in one of the three series of trials each subject performed. A strong decreasing RT–-ISI relationship was observed supporting the main hypothesis. However, a clear increase of mean RT over all ISIs combined, was also found. Because these two mixed effects were greatest when the click intervened at the possible times of ES occurrence only, three functions of time-information given by the click are discussed: (a) a reduction of the usual increase of time estimation error with increased ISI; (b) an increase of the subjects knowledge of the ISI range resulting from the discontinuity of the time-marking click which makes easier a discrete time-intervals numbering process; (c) a change of the simple-RT task into a discrimination task.

Crashworthiness optimization of new thin-walled cellular configurations

2014 ◽  
Vol 31 (5) ◽  
pp. 879-897 ◽  
Author(s):  
Shujuan Hou ◽  
Zhidan Zhang ◽  
Xujing Yang ◽  
Hanfeng Yin ◽  
Qing Li
Keyword(s):  
Factorial Design ◽  
Parametric Design ◽  
Vehicle Body ◽  
Factor Screening ◽  
Content Type ◽  
Crashworthiness Optimization ◽  
Design Variables ◽  
Rectangular Distribution ◽  
Optimal Criterion ◽  
Thin Walled

Purpose – The purpose of this paper is to optimize a new thin-walled cellular configurations with crashworthiness criteria, so as to improve the crashworthiness of components of a vehicle body. Design/methodology/approach – ANSYS Parametric Design Language is used to create the parameterized models so that the design variables can be changed conveniently. Moreover, the surrogate technique, namely response surface method, is adopted for fitting objective and constraint functions. The factorial design and D-optimal criterion are employed to screen active parameters for constructing the response functions of the specific energy absorption and the peak crushing force. Finally, sequential quadratic programming-NLPQL is utilized to solve the design optimization problem of the new cellular configurations filled with multi-cell circular tubes under the axial crushing loading. Findings – Two kinds of distribution modes of the cellular configurations are first investigated, which are in an orthogonal way and in a diamond fashion. After comparing the optimized configurations of the rectangular distribution with the annular distribution of the multi-cell fillers, it is found that the orthogonal way seems better in the aspects of crashworthiness than the diamond fashion. Originality/value – The two new thin-walled cellular configuration are studied and optimized with the crashworthiness criteria. Study on the new cellular configurations is very valuable for improving the crashworthiness of components of a vehicle body. Meanwhile, the factorial design and the factor screening are adopted in the process of the crashworthiness optimization of the new thin-walled cellular configurations.

scholarly journals On the Folding of the Rectangular Distribution

2013 ◽  
Vol 53 (1) ◽  
pp. 105-116
Author(s):  
S.A. El-Shehawy ◽  
M. Basher
Keyword(s):  
Rectangular Distribution
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