The form-transformation of the abdomen of the female pea-crab, Pinnotheres pisum Leach

1950 ◽  
Vol 137 (886) ◽  
pp. 115-136 ◽  
Keyword(s):  
Transformation Method ◽  
Continuous Functions ◽  
Residual Variance ◽  
Higher Power ◽  
Present Context ◽  
Pea Crab ◽  
Width Measurements ◽  
Definition Of ◽  
Affine Set ◽  
Form Transformation

The growth in width ( W ) of the segments of the abdomen relative to carapace size ( S ), and the graded distribution of growth along the abdomen, are analyzed by the method of fitting, to the observed values of W , polynomial regressions of progressively higher power in S . The simplest (linear) relation reveals the main features and each closer approximation furnishes further detail. The second object of the method, to select the lowest power of polynomial which adequately represents the data, gives the quadratic, though it is found that its adequacy varies in the different segments, which demand, for uniform adequacy, a non-affine set of polynomials. Adequacy is determined from the residual variance. The set of quadratics for the seven segments of the abdomen are combined, by a modification of Medawar’s transformation method, to give a single key relation which, within the scope of the data, defines abdomen width completely, spatially and temporally. This step involves the definition of the parameters of the quadratics as continuous functions of abdomen width at selected body size. It is suggested that the key relation to the transformation might, by analogy, be termed the ‘form-cinematogram’ for abdomen width. The equation: ‘form = shape+size’ is useful in the present context and is advocated for general recognition. The ‘shape-cinematogram’ may be derived from the form-cinematogram . Alternative attempts to derive a satisfactory form-cinematogram from the data are outlined. The form change is surprisingly simplified by the excision of the initial width measurements from all subsequent width measurements. The overall change in shape of the abdomen is visualized by the co-ordinate transformation method applied reciprocally between initial and final proportions.

scholarly journals Strong submeasures and applications to non-compact dynamical systems

2020 ◽  
pp. 1-23
Author(s):  
TUYEN TRUNG TRUONG
Keyword(s):  
Metric Space ◽  
Bounded Operator ◽  
Continuous Functions ◽  
Open Dense Subset ◽  
Compact Metric Space ◽  
Basic Properties ◽  
Banach Theorem ◽  
Complex Varieties ◽  
Definition Of ◽  
Meromorphic Maps

Abstract A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By the Hahn–Banach theorem, a positive strong submeasure is the supremum of a non-empty collection of measures whose masses are uniformly bounded from above. There are many natural examples of continuous maps of the form $f:U\rightarrow X$ , where X is a compact metric space and $U\subset X$ is an open-dense subset, where f cannot extend to a reasonable function on X. We can mention cases such as transcendental maps of $\mathbb {C}$ , meromorphic maps on compact complex varieties, or continuous self-maps $f:U\rightarrow U$ of a dense open subset $U\subset X$ where X is a compact metric space. For the aforementioned mentioned the use of measures is not sufficient to establish the basic properties of ergodic theory, such as the existence of invariant measures or a reasonable definition of measure-theoretic entropy and topological entropy. In this paper we show that strong submeasures can be used to completely resolve the issue and establish these basic properties. In another paper we apply strong submeasures to the intersection of positive closed $(1,1)$ currents on compact Kähler manifolds.

scholarly journals The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space

2013 ◽  
Vol 21 (3) ◽  
pp. 185-191
Author(s):  
Keiko Narita ◽  
Noboru Endou ◽  
Yasunari Shidama
Keyword(s):  
Banach Space ◽  
Integral Operator ◽  
Real Banach Space ◽  
Closed Interval ◽  
Continuous Functions ◽  
Real Numbers ◽  
Riemann Integral ◽  
Basic Properties ◽  
Bounded Functions ◽  
Definition Of

Summary In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems introduced in the article [9] and the article [11] to the proof. Using the definition of the article [10], we also proved some theorems on bounded functions.

The Private Hopes of American Fundamentalists and Evangelicals, 1925-1975

1991 ◽  
Vol 1 (2) ◽  
pp. 155-175 ◽  
Author(s):  
David Harrington Watt
Keyword(s):  
National Association ◽  
Moody Bible Institute ◽  
Recent Scholarship ◽  
Conservative Protestantism ◽  
Billy Graham ◽  
Present Context ◽  
Fundamentalist Movement ◽  
Definition Of ◽  
Born Again ◽  
National Association Of Evangelicals

Much of the best recent scholarship on conservative Protestantism in the middle decades of this Century focuses on what is sometimes called the “mainstream” of interdenominational evangelicalism. Although this variety of evangelicalism was deeply influenced by and, indeed, in some respects the direct successor to the fundamentalist movement of the 1910's, 1920's, and 1930's, it did not begin to assume its present shape until the early 1940's. The formation of the National Association of Evangelicals in 1942 is a convenient symbol of the emergence of what we now think of as constituting the evangelical mainstream.Drafting a perfect definition of this mainstream is impossible; drafting a good working description of it is not. In the present context, “evangelical mainstream” simply refers to that network of born-again Christians associated with the Billy Graham Evangelistic Association, the National Association of Evangelicals, and Campus Crusade for Christ; with schools such as the Moody Bible Institute, Füller Seminary, and Wheaton College; with publishing firms like Eerdman's and Zondervan; and with magazines such as Christianity Today, Eternity, and Moody Monthly.

The Weakening of Ideological Influences upon Soviet Design

Slavic Review ◽  
1968 ◽  
Vol 27 (1) ◽  
pp. 71-84 ◽  
Author(s):  
Raymond Hutchings
Keyword(s):  
Communist Party ◽  
Fine Arts ◽  
The Body ◽  
Detailed Consideration ◽  
Extended Treatment ◽  
Visual Form ◽  
Complex Approach ◽  
Present Context ◽  
Soviet Ideology ◽  
Definition Of

In this Article I shall examine the visual form or appearance (shape, size, and other visible qualities) of Soviet socially produced things (excluding any detailed consideration of trends in the fine arts or of individual craftsmanship) in relation to forces in Soviet ideology which seem to have influenced this form or appearance. (I do not attempt to describe all influences which bear on Soviet design, which would require a much more complex approach and a more extended treatment.) My definition of Soviet “ideology” would be the same as Professor Meyer's: the body of doctrine that is taught by the Communist Party to all Soviet citizens. Whether or not this doctrine is true, or thought to be true, as well as why it is propagated, or whether this would be a complete definition—these questions are considered to be irrelevant in the present context.

scholarly journals Boundaries in digital planes

1990 ◽  
Vol 3 (1) ◽  
pp. 27-55 ◽  
Author(s):  
Efim Khalimsky ◽  
Ralph Kopperman ◽  
Paul R. Meyer
Keyword(s):  
Jordan Curve ◽  
Ordered Set ◽  
Continuous Functions ◽  
Jordan Curve Theorem ◽  
Connected Sets ◽  
Digital Plane ◽  
Parameter Interval ◽  
Totally Ordered Set ◽  
Definition Of ◽  
Natural Way

The importance of topological connectedness properties in processing digital pictures is well known. A natural way to begin a theory for this is to give a definition of connectedness for subsets of a digital plane which allows one to prove a Jordan curve theorem. The generally accepted approach to this has been a non-topological Jordan curve theorem which requires two different definitions, 4-connectedness, and 8-connectedness, one for the curve and the other for its complement.In [KKM] we introduced a purely topological context for a digital plane and proved a Jordan curve theorem. The present paper gives a topological proof of the non-topological Jordan curve theorem mentioned above and extends our previous work by considering some questions associated with image processing:How do more complicated curves separate the digital plane into connected sets? Conversely given a partition of the digital plane into connected sets, what are the boundaries like and how can we recover them? Our construction gives a unified answer to these questions.The crucial step in making our approach topological is to utilize a natural connected topology on a finite, totally ordered set; the topologies on the digital spaces are then just the associated product topologies. Furthermore, this permits us to define path, arc, and curve as certain continuous functions on such a parameter interval.

scholarly journals Switching Point Solution of Second-Order Fuzzy Differential Equations Using Differential Transformation Method

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 231 ◽  
Author(s):  
Nadeem Salamat ◽  
Muhammad Mustahsan ◽  
Malik Saad Missen
Keyword(s):  
Differential Equations ◽  
Numerical Technique ◽  
Transformation Method ◽  
Higher Order ◽  
Differential Transformation Method ◽  
Fuzzy Differential Equation ◽  
Differential Transformation ◽  
Point Solution ◽  
Definition Of ◽  
Higher Order Differential Equations

The first-order fuzzy differential equation has two possible solutions depending on the definition of differentiability. The definition of differentiability changes as the product of the function and its first derivative changes its sign. This switching of the derivative’s definition is handled with the application of min, max operators. In this paper, a numerical technique for solving fuzzy initial value problems is extended to solving higher-order fuzzy differential equations. Fuzzy Taylor series is used to develop the fuzzy differential transformation method for solving this problem. This leads to a single solution for higher-order differential equations.

A kinematic investigation of a spherical involute bevel-geared system

2010 ◽  
Vol 224 (6) ◽  
pp. 1335-1348 ◽  
Author(s):  
H W Lee ◽  
K O Lee ◽  
D H Chung
Keyword(s):  
Azimuthal Angle ◽  
Cone Angle ◽  
Transformation Method ◽  
Bevel Gear ◽  
Operating Pressure ◽  
Number Of Teeth ◽  
Operating Rate ◽  
Shaft Angle ◽  
Definition Of ◽  
Coordinate Transformation Method

This study gives an exact definition of the spherical involute curved face and the pitch azimuthal angle of a bevel-geared system. Using the coordinate-transformation method, it derives the kinematic relations between the operating pressure angles, pitch azimuthal angles, operating pitch cone angles, base cone angles, and pitch action angles. An exact spherical involute bevel gear illustrates that a spherical involute tooth profile can be modelled only if the operating pressure angle, operating pitch cone angle, number of teeth, and cone radius are given. The ratio of the angular speeds of the spherical involute bevel gear reveals that the comparison of a bevel gear with a cone friction wheel is similar to the situation in which a belt that is wound around a base cone becomes untied and is wound around the base cone of the other party. The findings confirm that even when the shaft angle changes, the ratio of angular speeds does not change. This study also exactly calculates the operating rate in an involute bevel gear in a theoretical manner. To review interchangeability, the study defines the angular pitch and the crown number of teeth and shows that the proposed spherical involute bevel gear possesses interchangeability. To verify the contact phenomenon of the spherical involute bevel gear, a computer-graphic verification is conducted on three models to see whether gear interference occurs when two gears are operating while going in gear with each other.

scholarly journals Remarks on uniformly symmetrically continuous functions

2016 ◽  
Vol 09 (03) ◽  
pp. 1650069
Author(s):  
Tammatada Khemaratchatakumthorn ◽  
Prapanpong Pongsriiam
Keyword(s):  
Real Line ◽  
Nonempty Subset ◽  
Continuous Functions ◽  
The Real ◽  
Definition Of ◽  
Symmetrically Continuous Functions ◽  
Uniformly Continuous

We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of symmetrically continuous functions and uniformly continuous functions. We obtain some characterizations of uniformly symmetrically continuous functions. Several examples are also given.

Quasistationary distributions for continuous time Markov chains when absorption is not certain

1999 ◽  
Vol 36 (01) ◽  
pp. 268-272 ◽  
Author(s):  
P. K. Pollett
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Initial Distribution ◽  
Probabilistic Interpretation ◽  
Continuous Time Markov Chains ◽  
Absorbing Markov Chains ◽  
Present Context ◽  
Conditional State ◽  
Quasistationary Distributions ◽  
Definition Of

Recently, Elmes et al. (see [2]) proposed a definition of a quasistationary distribution to accommodate absorbing Markov chains for which absorption occurs with probability less than 1. We will show that the probabilistic interpretation pertaining to cases where absorption is certain (see [13]) does not hold in the present context. We prove that the state probabilities at time t conditional on absorption taking place after t, generally depend on t. Conditions are derived under which there is no initial distribution such that the conditional state probabilities are stationary.

scholarly journals High resolution VHF radar measurements of tropopause structure and variability at Davis, Antarctica (69° S, 78° E)

2012 ◽  
Vol 12 (10) ◽  
pp. 26173-26205 ◽  
Author(s):  
S. P. Alexander ◽  
D. J. Murphy ◽  
A. R. Klekociuk
Keyword(s):  
Lapse Rate ◽  
Winter Period ◽  
Summer Period ◽  
Vhf Radar ◽  
Power Spectral ◽  
Higher Power ◽  
Radar Echo ◽  
Radar Measurements ◽  
Definition Of ◽  
The Antarctic

Abstract. Two years of VHF radar echo power observations are used to examine the structure and variability of the tropopause at Davis, Antarctica. Co-located radiosonde and ozonesonde launches provide data with which to calculate the thermal (lapse-rate) and chemical tropopauses at Davis. The dynamically-controlled radar tropopause can be used as a definition of the Antarctic tropopause throughout the year under all meteorological conditions. During the extended summer period of December–April (DJFMA) inclusive, radar tropopauses are (0.2 ± 0.4) km lower than co-located radiosonde thermal tropopauses and during the extended winter period of June–October (JJASO) inclusive, the radar tropopauses are (0.8 ± 1.0) km lower. The radar and ozone tropopauses both show a decrease in altitude under increasingly strong cyclonic conditions. During strong JJASO cyclonic conditions, there are large (several km) differences between radiosonde lapse-rate tropopause altitudes and radar tropopause altitudes. However, the radar tropopause altitude closely corresponds to the altitude of the 2 PVU surface (where 1 PVU = 106 m2 s−1 K kg−1) for both cyclonic and anticyclonic conditions. The monthly mean occurrence frequency of tropopause folds is investigated using the radar tropopause and is about 1 per month during DJFMA and about 3 per month during JJASO. The power spectrum of the Davis radar tropopause altitude indicates its influence by the passage of inertio-gravity waves. The higher power spectral density during JJASO also indicates an increase in gravity wave activity during this time.

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