APPROXIMATION TO THE LATERAL VARIATION OF RESIDUAL GRAVITY DUE TO A FRUSTUM OF A VERTICAL CONE

Geophysics ◽  
1953 ◽  
Vol 18 (2) ◽  
pp. 401-415
Author(s):  
W. Raymond Griffin
Keyword(s):  
Gulf Coast ◽  
Lateral Variation ◽  
Vertical Cone ◽  
Salt Domes ◽  
Residual Gravity ◽  
Special Cases ◽  
Lateral Distance ◽  
Independent Variable ◽  
The Subject ◽  
Two Parameters

The equation for the subject title is presented in nondimensional form. The approximation consists of considering a frustum of a vertical cone in which the radii are small relative to the depth to its top. The dependent variable has been taken as being the ratio of the residual gravity (as defined in a previous publication by the author) to the maximum residual gravity. The independent variable was chosen as the ratio of the lateral distance (from the center line of the frustum to a given station) to the depth to the top of the frustum. The two parameters were chosen as being (a) The ratio of depth to the bottom of the frustum to that to its top, (b) The ratio of the bottom radius to that of the top radius. It is then shown that, for special values of the parameters, the equation gives the lateral variation of residual gravity due to cylinders, upright cones, and inverted cones as special cases. Tables of the principal functions, which occur in the equation, are given over practical ranges of values. Graphs of the equation are given. They cover the practical range for each of the variables and each of the parameters. Application of the equation is made to two Gulf Coast salt domes whose dimensions are rather well known from previous drilling. Graphs, showing the degree of correlation, are given. The conclusion is drawn that, despite the approximation involved in the derivation of the equation, and despite the departure of the ratio of the dimensions of the salt domes from that assumed, the correlation with the actual gravity values for two deep salt domes is remarkably close.

scholarly journals Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

Model Theory: Geometrical and Set-Theoretic Aspects and Prospects

2003 ◽  
Vol 9 (2) ◽  
pp. 197-212 ◽  
Author(s):  
Angus Macintyre
Keyword(s):  
Model Theory ◽  
Category Theory ◽  
Theoretic Model ◽  
Topos Theory ◽  
Sheaf Theory ◽  
Special Cases ◽  
Algebraic Spaces ◽  
The Subject ◽  
Near Future ◽  
Modern Mathematics

I see model theory as becoming increasingly detached from set theory, and the Tarskian notion of set-theoretic model being no longer central to model theory. In much of modern mathematics, the set-theoretic component is of minor interest, and basic notions are geometric or category-theoretic. In algebraic geometry, schemes or algebraic spaces are the basic notions, with the older “sets of points in affine or projective space” no more than restrictive special cases. The basic notions may be given sheaf-theoretically, or functorially. To understand in depth the historically important affine cases, one does best to work with more general schemes. The resulting relativization and “transfer of structure” is incomparably more flexible and powerful than anything yet known in “set-theoretic model theory”.It seems to me now uncontroversial to see the fine structure of definitions as becoming the central concern of model theory, to the extent that one can easily imagine the subject being called “Definability Theory” in the near future.Tarski's set-theoretic foundational formulations are still favoured by the majority of model-theorists, and evolution towards a more suggestive language has been perplexingly slow. None of the main texts uses in any nontrivial way the language of category theory, far less sheaf theory or topos theory. Given that the most notable interactions of model theory with geometry are in areas of geometry where the language of sheaves is almost indispensable (to the geometers), this is a curious situation, and I find it hard to imagine that it will not change soon, and rapidly.

Unification of Software Reliability Models by Self-Exciting Point Processes

1997 ◽  
Vol 29 (2) ◽  
pp. 337-352 ◽  
Author(s):  
Yiping Chen ◽  
Nozer D. Singpurwalla
Keyword(s):  
Software Reliability ◽  
Point Processes ◽  
Computer Software ◽  
Probability Models ◽  
Reliability Models ◽  
Common Structure ◽  
Software Reliability Models ◽  
Special Cases ◽  
Active Debate ◽  
The Subject

Assessing the reliability of computer software has been an active area of research in computer science for the past twenty years. To date, well over a hundred probability models for software reliability have been proposed. These models have been motivated by seemingly unrelated arguments and have been the subject of active debate and discussion. In the meantime, the search for an ideal model continues to be pursued. The purpose of this paper is to point out that practically all the proposed models for software reliability are special cases of self-exciting point processes. This perspective unifies the very diverse approaches to modeling reliability growth and provides a common structure under which problems of software reliability can be discussed.

scholarly journals Pengaruh Pemberian Tepung Tempe terhadap Kadar Kolesterol Total Darah Mencit (Mus musculus) Hiperkolesterol

bionature ◽  
2019 ◽  
Vol 20 (2) ◽  
pp. 116
Author(s):  
Heryl Rumtal ◽  
Rosdiana Ngitung ◽  
A. Mu’nisa A. Mu’nisa
Keyword(s):  
Mus Musculus ◽  
Blood Cholesterol ◽  
Cholesterol Concentration ◽  
Total Blood ◽  
Treatment Groups ◽  
Independent Variable ◽  
The Subject ◽  
Imprinting Control Region ◽  
Total Blood Cholesterol ◽  
Research Show

Abstract. This research is experimental which aims to determine the effect of giving Tempe Flour to total blood cholesterol concentration of hypercholesterol mice (Mus musculus). The independent variable of this research Tempe Flour while the dependent variable is the total blood cholesterol concentration of mice (Mus musculus). The subject of this research is 25 male ICR strain (Imprinting Control Region) mice with 3 months age divided 5 treatment groups which are normal group, hypercholesterol group, giving of tempe flour at dose of 10 g / day / BB (P1), 20 g / days / BB (P2) and 25 g / day / BB (P3). Tempe flour is given after the giving of cholesterol feed. All mices blood cholesterol concentration were check after the time of treatment. The result is analyz by using ANOVA with Ducan test. The result of this research show that the giving of Tempe Flour affected the decrease of blood cholesterol concentration of mice (Mus musculus) in dose of 10 g/day/BB,20 g/day/BB and 25 g/day/BB. Dose of 25 g/day/BB showed an effective dose for lowering cholesterol in the research.   Keywords: tempe flour, cholesterol, hypercholesterol, mencit (Mus musculus)

Occurrence of gypsum in Gulf coast salt domes

1922 ◽  
Vol 17 (2) ◽  
pp. 141-143
Author(s):  
Donald Clinton Barton
Keyword(s):  
Gulf Coast ◽  
Salt Domes
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