scholarly journals ON INVERSE OF A REGULAR SURFACE WITH RESPECT TO THE UNIT SPHERE S2 IN E3

2021 ◽  
Vol 21 (1) ◽  
pp. 171-198
Author(s):  
SIDIKA TUL ◽  
FERAY BAYAR ◽  
AYHAN SARIOĞLUGİL
Keyword(s):  
Unit Sphere ◽  
Regular Surface ◽  
Original Surface ◽  
Algebraic Invariants ◽  
Software Program ◽  
Definition Of

The purpose of this paper, first, is to give a definition of the inverse surface of a given regular surface with respect to a unit sphere in E3. Second, some characteristic properties of the inverse surface are to express depending on the algebraic invariants of the original surface. In the last part of the study, we gave examples supporting our claims and plotted their graphics with the help of Maple software program.

scholarly journals A new look at the Bondi-Sachs energy-momentum

2021 ◽  
Author(s):  
Jörg Frauendiener ◽  
Chris Stevens
Keyword(s):  
Unit Sphere ◽  
Gauss Curvature ◽  
Null Infinity ◽  
Conformally Invariant ◽  
Lorentzian Metric ◽  
Correct Definition ◽  
Ghp Formalism ◽  
Bondi Mass ◽  
Definition Of ◽  
Bondi Energy

Abstract How does one compute the Bondi mass on an arbitrary cut of null infinity I when it is not presented in a Bondi system? What then is the correct definition of the mass aspect? How does one normalise an asymptotic translation computed on a cut which is not equipped with the unit-sphere metric? These are questions which need to be answered if one wants to calculate the Bondi-Sachs energy-momentum for a space-time which has been determined numerically. Under such conditions there is not much control over the presentation of I so that most of the available formulations of the Bondi energy-momentum simply do not apply. The purpose of this article is to provide the necessary background for a manifestly conformally invariant and gauge independent formulation of the Bondi energy-momentum. To this end we introduce a conformally invariant version of the GHP formalism to rephrase all the well-known formulae. This leads us to natural definitions for the space of asymptotic translations with its Lorentzian metric, for the Bondi news and the mass-aspect. A major role in these developments is played by the “co-curvature”, a naturally appearing quantity closely related to the Gauß curvature on a cut of I.

scholarly journals On the Blaschke approach of ruled surface

2003 ◽  
Vol 34 (2) ◽  
pp. 107-116 ◽  
Author(s):  
Rashad A. Abdel Baky
Keyword(s):  
Unit Sphere ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Necessary Condition ◽  
Original Surface ◽  
Distribution Parameters ◽  
Local Properties

In this paper using E. Study map and the Blaschke approach we studied a ruled surface as a curve on the dual unit sphere. The Blaschke approach proceeds by defining a sequence of ruled surfaces associated with the ruled surface. The relative positions of these surfaces and their distribution parameters characterize the local properties of the original surface. A necessary condition for a ruled surface to be closed is derived. Moreover, an example of application is investigated in detail.

scholarly journals Preparing Auditors for the Blockchain Oracle Problem

2021 ◽  
Author(s):  
Mark D. Sheldon
Keyword(s):  
Information Systems ◽  
Service Organization ◽  
Working Definition ◽  
Smart Contract ◽  
Auditing Standards ◽  
Software Program ◽  
Definition Of

This article summarizes “Auditing the blockchain oracle problem” (Sheldon 2021), which introduces auditors to the risks of having an irreversible business agreement codified on a blockchain using a short software program called a smart contract, that relies on an oracle to provide information from outside the blockchain in order to execute correctly. The article begins with an explanation of the role that oracles play in the blockchain ecosystem and proposes a working definition of oracles. Next, the article highlights how the auditing standards from both the AICPA and PCAOB can be interpreted to classify an oracle as part of smart contract users’ information systems, and that the oracle provides a robust set of services that qualify it as a service organization. Finally, the article describes the process used by an oracle to collect, store, transform, and transmit data and highlights relevant risks and illustrative control objectives related to this process.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Symbiotic Stars at Optical, Infrared and Radio Wavelengths

1979 ◽  
Vol 46 ◽  
pp. 125-149 ◽  
Author(s):  
David A. Allen
Keyword(s):  
Temperature Regime ◽  
Type Star ◽  
Stellar Systems ◽  
Symbiotic Stars ◽  
Lower Excitation ◽  
Definition Of ◽  
Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

Immunoferritin localization of intracellular antigens in positively stained frozen sections

1978 ◽  
Vol 36 (2) ◽  
pp. 168-169
Author(s):  
K. T. Tokuyasu
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Thin Layers ◽  
The Other ◽  
Positive Staining ◽  
Frozen Sections ◽  
The Past ◽  
Ultrathin Frozen Sections ◽  
Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

Initial Polymerization Sites Indicated During Mitochondrial Oxidation of Diaminobenzidine after Toluene Treatment

1977 ◽  
Vol 35 ◽  
pp. 408-409
Author(s):  
W. A. Shannon ◽  
M. A. Matlib
Keyword(s):  
Membrane Permeability ◽  
Cytochrome Oxidase ◽  
Rat Liver ◽  
Precise Definition ◽  
Cytochemical Localization ◽  
Oxidative Reaction ◽  
Mitochondrial Oxidation ◽  
Definition Of ◽  
Exogenous Substrates

Numerous studies have dealt with the cytochemical localization of cytochrome oxidase via cytochrome c. More recent studies have dealt with indicating initial foci of this reaction by altering incubation pH (1) or postosmication procedure (2,3). The following study is an attempt to locate such foci by altering membrane permeability. It is thought that such alterations within the limits of maintaining morphological integrity of the membranes will ease the entry of exogenous substrates resulting in a much quicker oxidation and subsequently a more precise definition of the oxidative reaction.The diaminobenzidine (DAB) method of Seligman et al. (4) was used. Minced pieces of rat liver were incubated for 1 hr following toluene treatment (5,6). Experimental variations consisted of incubating fixed or unfixed tissues treated with toluene and unfixed tissues treated with toluene and subsequently fixed.

Application of Scanning Electron Microscopy to Medical Research

1969 ◽  
Vol 27 ◽  
pp. 12-13
Author(s):  
J. D. Hutchison
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Medical Research ◽  
Prosthetic Heart Valve ◽  
School Of Medicine ◽  
Transmission Electron ◽  
Definition Of ◽  
Mechanism Of Failure ◽  
The Brain ◽  
Scanning Electron

When the transmission electron microscope was commercially introduced a few years ago, it was heralded as one of the most significant aids to medical research of the century. It continues to occupy that niche; however, the scanning electron microscope is gaining rapidly in relative importance as it fills the gap between conventional optical microscopy and transmission electron microscopy.IBM Boulder is conducting three major programs in cooperation with the Colorado School of Medicine. These are the study of the mechanism of failure of the prosthetic heart valve, the study of the ultrastructure of lung tissue, and the definition of the function of the cilia of the ventricular ependyma of the brain.

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