A MATHEMATICAL ANALYSIS OF THE DISTRIBUTION IN MAIZE OF HELIOTHIS ARMIGERA Hb. (OBSOLETA F.)

1942 ◽  
Vol 20d (8) ◽  
pp. 235-261 ◽  
Author(s):  
Marjory G. Walker
Keyword(s):  
Mathematical Analysis ◽  
Mathematical Theory ◽  
Random Distribution ◽  
Heliothis Armigera ◽  
The Other ◽  
Good Representation ◽  
Poisson Series ◽  
Egg Distribution ◽  
Rough Approximation ◽  
Maize Plants

The distribution among maize plants of the eggs of the American boll-worm, Heliothis armigera Hb., is discussed and analysed.The problem is considered in relation lo what is known of the connection between the state of development of maize plants and their attractiveness to ovipositing boll-worm moths. The actual frequency distribution of the eggs suggests a random as opposed to a uniform distribution, but it is shown that the conditions required for a pure mathematical random distribution cannot be satisfied. Because the maize plants differ from one another in absolute degree of attractiveness at any one time, and in relative degree of attractiveness with the passing of time, it is not true that every plant has the same chance of receiving any given egg.It is demonstrated that a mathematical theory, which is eventually one of random distribution, but which incorporates a modification to allow for the varying degrees of attractiveness of the plants, gives a fairly good representation of the egg distribution found in the field.Theoretical distributions to fit the data are calculated by two methods. One is a discontinuous process which is presented as only a rough approximation of what it is intended lo express. The other uses the compound Poisson series of Greenwood and Yule. The continuous variation in nature both in space and time, which is the essential difficulty of the problem, is discussed.

scholarly journals Autonomously Replicating Macronuclear DNA Pieces Are the Physical Basis of Genetic Coassortment Groups in Tetrahymena thermophila

Genetics ◽  
2000 ◽  
Vol 155 (3) ◽  
pp. 1119-1125
Author(s):  
Laura Wong ◽  
Lana Klionsky ◽  
Steve Wickert ◽  
Virginia Merriam ◽  
Eduardo Orias ◽  
...  
Keyword(s):  
Random Distribution ◽  
Tetrahymena Thermophila ◽  
Physical Basis ◽  
The Other ◽  
Site Specific ◽  
Phenotypic Assortment ◽  
Somatic Genome

Abstract The macronucleus of the ciliate Tetrahymena thermophila contains a fragmented somatic genome consisting of several hundred identifiable chromosome pieces. These pieces are generated by site-specific fragmentation of the germline chromosomes and most of them are represented at an average of 45 copies per macronucleus. In the course of successive divisions of an initially heterozygous macronucleus, the random distribution of alleles of loci carried on these copies eventually generates macronuclei that are pure for one allele or the other. This phenomenon is called phenotypic assortment. We have previously reported the existence of loci that assort together (coassort) and hypothesized that these loci reside on the same macronuclear piece. The work reported here provides new, rigorous genetic support for the hypothesis that macronuclear autonomously replicating chromosome pieces are the physical basis of coassortment groups. Thus, coassortment allows the mapping of the somatic genome by purely genetic means. The data also strongly suggest that the random distribution of alleles in the Tetrahymena macronucleus is due to the random distribution of the MAC chromosome pieces that carry them.

The Theory and Prevention of Undamped Aeroplane Nosewheel Shimmy

1956 ◽  
Vol 7 (3) ◽  
pp. 193-220
Author(s):  
D. Williams
Keyword(s):  
Mathematical Theory ◽  
The Other ◽  
Linkage Mechanism ◽  
Model Experiments ◽  
Good Feature ◽  
The One ◽  
Value Model ◽  
Elastic Constraint

SummaryThe mathematical theory of nosewheel shimmy is given, with particular reference to twin nosewheel assemblies. It is shown that a sovereign remedy for shimmy is to make the castor length greater than what is here called the “ creep distance,” which in practice is found to be approximately equal to the tyre radius. Lateral flexibility of the oleo leg is disadvantageous but elastic constraint at the pivot is a good feature. The one necessitates an increased castor for stability while the other allows a smaller castor. It is also shown how, by the use of a compact linkage mechanism, the effective castor length can be made independent of the wheel-leg offset and can have any desired value. Model experiments that confirm the theoretical conclusions are described.

scholarly journals Difficulties and modifications in the use of available methods for hydraulic conductivity measurements in highly clogged horizontal subsurface flow constructed wetlands

2017 ◽  
Vol 76 (7) ◽  
pp. 1666-1675 ◽  
Author(s):  
Mateus Pimentel Matos ◽  
André Baxter Barreto ◽  
Gabriel Rodrigues Vasconcellos ◽  
Antonio Teixeira Matos ◽  
Gustavo Ferreira Simões ◽  
...  
Keyword(s):  
Hydraulic Conductivity ◽  
Constructed Wetlands ◽  
Subsurface Flow ◽  
The Other ◽  
Good Representation ◽  
Horizontal Distance ◽  
Conductivity Measurements ◽  
Construction Time ◽  
Horizontal Subsurface Flow ◽  
Subsurface Flow Constructed Wetlands

Despite the fact that several authors consider the available measurement methods of hydraulic conductivity (ks) suitable for a good representation of the bed condition and clogging potential in horizontal subsurface flow constructed wetlands, others have questioned their adequacy. In this work, hydraulic conductivity measurements with conventional and modified methods were undertaken in two small full-scale units, one planted with cattail (Typha latifolia) and the other unplanted. Both units had already been operating for seven years and showed a high degree of clogging. It was observed that the use of the falling head method, with the introduction of the tubes during the test, provided results without a clear spatial trend. On the other hand, tests done on monitoring wells inserted during construction time showed, as expected, ks increasing with the horizontal distance from the inlet, but without reflecting actual field conditions. It was observed that, as the bed became more clogged, the use of the reported methods became more complex, suggesting the need of other methodologies. The use of planted fixed reactors (removable baskets installed in the bed) with evaluation of ks at constant head in the laboratory showed potential for the characterization of the hydrodynamic properties of the porous medium.

Mathematical Analysis on Helicoids Architectural Form

2013 ◽  
Vol 790 ◽  
pp. 273-277
Author(s):  
Zhong Yi ◽  
Cheng Zhi Yuan
Keyword(s):  
Mathematical Analysis ◽  
Mathematical Theory ◽  
Architecture Design ◽  
Curved Surfaces ◽  
Mathematical Transformation ◽  
Geometric Figure ◽  
Topological Transformation ◽  
Architectural Form ◽  
Geometric Figures ◽  
Architecture Modeling

In a sense, architecture may be called as a geometric figure. Although architectural forms are very different, the form from one kind of architecture to another kind of architecture is equivalent to one kind of mathematical transformation in view of mathematics; for example, the transformation between a cube architecture and a spherical architecture belongs to a topological transformation. Currently, many sculptural features appear in the architecture design, which may be called as the nonlinear architecture. Curves and curved surfaces are widely used in the architecture modeling. Moreover, functional spaces are divided inside the architecture shell according to requirements. Architects are inclined to use a mathematical theory especially the geometrical knowledge in an architecture design. However, architects can not imagine many artistic geometric figures in geometry. Besides, such wonderful geometric figures always include some miraculous mathematical and physical properties.

scholarly journals Statistical analysis of chromosome distribution to the poles in interspecific hybrids with variable chromosome pairing

1963 ◽  
Vol 4 (2) ◽  
pp. 266-275 ◽  
Author(s):  
A. G. Sficas
Keyword(s):  
Statistical Analysis ◽  
Interspecific Hybrids ◽  
Random Distribution ◽  
The Other ◽  
Meiotic Pairing ◽  
Variable Amount ◽  
Short Discussion ◽  
Equal Distribution ◽  
Chromosome Separation ◽  
Opposite Tendency

A probability distribution of chromosome separation to the poles was developed to test the randomness of movement of univalents in asynaptic material where a variable amount of meiotic pairing occurs. Two tables were calculated, one for 24 chromosomes which can be used for any even number equal or less than 24, and the other for 19 chromosomes which can be used for any odd number equal or less than 19.Three Nicotiana hybrids, namely N. glutinosa × N. otophora, N. glutinosa, N. sylvestris, and N. tabacum × N. glutinosa, and one polyhaploid were investigated. All hybrids had a tendency towards an equal distribution of unpaired chromosomes to the poles. The polyhaploid N. tabacum (with a substituted N. plumbaginifolia chromosome) had an opposite tendency, i.e. towards a flatter distribution than expected from random distribution of univalents. A short discussion of the problem is given.

scholarly journals Markov chains and the determination of fair premiums

1967 ◽  
Vol 4 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Stefan Vajda
Keyword(s):  
Stochastic Process ◽  
Markov Chains ◽  
Stochastic Processes ◽  
Mathematical Theory ◽  
The Other ◽  
Main Stream ◽  
Other Hand ◽  
Pure Mathematics ◽  
The University

The relationships between actuarial and pure mathematics are curious. Actuaries have contributed to the development of mathematical theory: it is sufficient to mention, as examples, Fredholm of an earlier, and Cramér of a more recent generation. Scandinavian mathematicians, in particular, have been concerned with a very special type of stochastic process, reflected in the collective theory of risk, and the work of Philipson, Ammeter and others in this field is well known to readers of this Bulletin. However, the main stream of the theory of stochastic processes has little contact with actuarial applications.On the other hand, many actuaries have studied and assimilated pure mathematics and have thrown light on actuarial matters by describing their own preoccupations in the terminology of modern, often abstract, mathematics. E. Franckx is one of their number.The Instituto di Matematica Finanziaria of the University of Trieste (Faculty of Economics and Commerce) has published a booklet entitledEssai d'une théorie opérationnelle des risques Markoviens which contains three lectures delivered by Professor Franckx in Trieste and a contribution which he presented to the 17th Congress of Actuaries, held in London in 1964.

Text and Illustration Based Scenario Expressions for Conveying Failure Knowledge

2004 ◽  
Author(s):  
Yotaro Hatamura ◽  
Kensuke Tsuchiya
Keyword(s):  
Prior Knowledge ◽  
The Other ◽  
Case Illustration ◽  
Good Representation ◽  
Good Image ◽  
Failure Event

Our “Study of Failure” has shown the effects of failure case illustration and text based diagonal scenario expression to successfully convey the essence of failure cases to the reader. A well drawn failure case illustration generates a good image of the failure event in the readers mind, thus succeeds in passing the failure knowledge to the reader. A carefully produced diagonal scenario expression has the same effect. We demonstrated the power of these two fundamentally different representations through an experiment: A failure case illustration alone was shown to a group of people who were asked to define a diagonal scenario expression for the case. The reverse test started from a diagonal scenario expression to reach an illustration that the group had no prior knowledge about. Our tests showed that people can produce a fairly good representation in the other form starting from either an illustration or a diagonal scenario alone.

Reviews - A. E. Heath. Preface. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 7–8. - R. Rhees. Note in editing. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 9–43. - George Boole. The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning. A reprint of 191. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 45–119. - George Boole. Later notes (to the foregoing). Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 119–124. (Taken from manuscript in the Library of the Royal Society.) - George Boole. The calculus of logic. A reprint of 192. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 125–140. - George Boole. Sketch of a theory and method of probabilities founded upon the calculus of logic. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 141–166. (From manuscripts in the Royal Society Library, probably before 1851.) - George Boole. Of propositions numerically definite. A reprint of 194. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 167–186. - George Boole. The claims of science, especially as founded in its relation to human nature. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 187–210. (Lecture published in London, 1851.) - George Boole. Logic and reasoning. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 211–229. (From Royal Society manuscripts, after 1855.) - George Boole. Extracts from a paper entitled “On the mathematical theory of logic and on the philosophical interpretation of its methods and processes.”Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 230–246. (From Royal Society manuscripts, later than 1855.)

1959 ◽  
Vol 24 (3) ◽  
pp. 203-209 ◽  
Author(s):  
Michael Dummett
Keyword(s):  
Mathematical Analysis ◽  
Royal Society ◽  
Mathematical Theory ◽  
Deductive Reasoning ◽  
Publishing Company ◽  
Philosophical Interpretation ◽  
Open Court ◽  
Court Publishing ◽  
George Boole ◽  
Nature Studies

The Mathematical Theory of the Snaking of Two-wheeled Trailers, with Practical Rules and Devices for Preventing Snaking

1951 ◽  
Vol 5 (1) ◽  
pp. 175-190 ◽  
Author(s):  
D. Williams
Keyword(s):  
General Solution ◽  
Detailed Analysis ◽  
Mathematical Analysis ◽  
Mathematical Theory ◽  
Degrees Of Freedom ◽  
Critical Speed ◽  
Elastic System ◽  
Practical Experience ◽  
Dynamical Equations ◽  
All Speeds

It is well known that a prime essential in bringing about unstable motion in any elastic system is the presence of at least two degrees of freedom. A trailer and its towing vehicle constitute a mechanical system with a number of degrees of freedom, and a main feature of the present problem is the necessity for deciding which are essential factors in the unstable motion and which are trivial or merely incidental. The idea of including all the possible degrees of freedom in the dynamical equations, thereby obtaining a general solution in which the part played by the several parameters can be seen, is quite impracticable. In Part I of the paper the results obtained from the mathematical analysis of the problem are given and discussed. There is a general agreement with practical experience. Part II contains the detailed analysis on which the conclusions in Part I are based. It is emphasized that the main purpose of the analysis is not to enable calculations to be made of the precise critical speed at which snaking begins for any particular combination of tractor and trailer, but to discover what factors make for stability and for instability, and how to design for immunity from snaking at all speeds.

Transect Fly-rounds in Field Studies of Glossina

1959 ◽  
Vol 50 (2) ◽  
pp. 275-285 ◽  
Author(s):  
J. Ford ◽  
J. P. Glasgow ◽  
D. L. Johns ◽  
J. R. Welch
Keyword(s):  
Quantitative Data ◽  
Field Studies ◽  
The Other ◽  
Line Transect ◽  
Tsetse Flies ◽  
Poisson Series ◽  
Nyanza Province ◽  
Similar Tendency ◽  
Straight Lines ◽  
Absolute Population

The fly-round has for long been regarded as the most satisfactory way of following fluctuations in populations of tsetse flies (Glossina) and locating areas of concentration. It consists of a path cut through bush so as to traverse the principal vegetation communities and is divided into sections, corresponding to the latter, on each of which the flies are caught. A modification now widely used but not previously described in detail is termed a line transect or transect fly-round; this follows an arbitrary course along straight lines that may be orientated with regard to the topography and is divided into numerous short sections of equal length terminating at posts at which flies are caught. In its simplest form it follows a straight course, but various patterns are used including an angular spiral. It facilitates the collection of quantitative data on tsetse density and the factors (such as vegetation) that affect it, and their analysis is possible in more detail than was the case when the fly-round was laid out according to a pre conceived notion of vegetational relationships. This is illustrated by data from a fly-round at Shinyanga, Tanganyika, consisting of six sides, each of 2,000 yd., of two diagonally adjoining squares, that was divided originally into nine sections of varying lengths representing the floristic communities traversed, and subse quently into 120 sections each 200 yd. long. Comparison of the catches of non-teneral males of G. swynnertoni Aust. grouped according to the two methods emphasises the much greater detail provided by the second of them. The transect fly-round is easy to lay out and operate and is thought likely to be particularly useful in connection with reclamation work.The effect of varying the section length was investigated for G. swynnertoni at Shinyanga, G. pallidipes Aust. in Nyanza Province, Kenya, and G. austeni Newst. in Zanzibar. With the first, progressively fewer flies of all categories except teneral males were caught as the section length was increased progressively from 50 to 200 yd.; with the other species a similar tendency was apparent, but not significant. The results emphasise a point long recognised but often neglected, that data from fly-rounds reflect, in part, the reaction of tsetse populations to the behaviour of the catching party. That this reaction, termed the availability, is itself inconstant is shown by catches of G. pallidipes on a fly-round done daily for a month, in which differences between catches on consecutive days, sometimes exceeding 3:1, must represent changes in availability, not in absolute population.Data from the transect fly-round can be analysed so as to indicate sections where the catches deviate significantly from those expected on the assumption that they are distributed according to a Poisson series, and where there may thus be presumed to be areas of concentration of the population, or the reverse. A Table is provided to facilitate such analysis.

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