scholarly journals Classification of Geometries with Projective Metric

1909 ◽  
Vol 28 ◽  
pp. 25-41 ◽  
Author(s):  
D. M. Y. Sommerville
Keyword(s):  
Dihedral Angle ◽  
Plane Geometry ◽  
Three Dimensions ◽  
Angular Measurement ◽  
Plane Angle ◽  
Degenerate Form ◽  
Projective Metric ◽  
The Absolute ◽  
Straight Lines

In the Cayley-Klein projective metric it is ordinarily assumed that the measure of angles, plane and dihedral, is always elliptic, i.e. in a sheaf of planes or lines there is no actual plane or line which makes an infinite angle with the others. With this restriction there are only three kinds of geometry—Parabolic, Hyperbolic and Elliptic, i.e. the geometries of Euclid, Lobachevskij and Riemann ; and the form of the absolute is also limited. Thus in plane geometry the only degenerate form of the absolute which is possible is two coincident straight lines and a pair of imaginary points ; in three dimensions the absolute cannot be a ruled quadric, other than two coincident planes. If, however, this restriction as to angular measurement is removed, there are 9 systems of plane geometry and 27 in three dimensions; for the measure of distance, plane angle and dihedral angle may be parabolic, hyperbolic, or elliptic.

Permeability-porosity transforms from small sandstone fragments

Geophysics ◽  
2006 ◽  
Vol 71 (1) ◽  
pp. N11-N19 ◽  
Author(s):  
Ayako Kameda ◽  
Jack Dvorkin ◽  
Youngseuk Keehm ◽  
Amos Nur ◽  
William Bosl
Keyword(s):  
Pore Space ◽  
Petroleum Industry ◽  
Rock Physics ◽  
Three Dimensions ◽  
Absolute Permeability ◽  
High Porosity ◽  
Drill Cuttings ◽  
Thin Sections ◽  
Numerical Experimentation ◽  
The Absolute

Numerical simulation of laboratory experiments on rocks, or digital rock physics, is an emerging field that may eventually benefit the petroleum industry. For numerical experimentation to find its way into the mainstream, it must be practical and easily repeatable — i.e., implemented on standard hardware and in real time. This condition reduces the size of a digital sample to just a few grains across. Also, small physical fragments of rock, such as cuttings, may be the only material available to produce digital images. Will the results be meaningful for a larger rock volume? To address this question, we use a number of natural and artificial medium- to high-porosity, well-sorted sandstones. The 3D microtomography volumes are obtained from each physical sample. Then, analogous to making thin sections of drill cuttings, we select a large number of small 2D slices from a 3D scan. As a result, a single physical sample produces hundreds of 2D virtual-drill-cuttings images. Corresponding 3D pore-space realizations are generated statistically from these 2D images; fluid flow is simulated in three dimensions, and the absolute permeability is computed. The results show that small fragments of medium– to high-porosity sandstones that are statistically subrepresentative of a larger sample will not yield the exact porosity and permeability of the sample. However, a significant number of small fragments will yield a site-specific permeability-porosity trend that can then be used to estimate the absolute permeability from independent porosity data obtained in the well or inferred from seismic techniques.

Geometric Characteristics of the Center-Point Curve Based on the Kinematics of the Compatibility Linkage

1992 ◽  
Author(s):  
J. A. Schaaf ◽  
J. A. Lammers
Keyword(s):  
Complex Number ◽  
Change Point ◽  
Double Point ◽  
Classification Scheme ◽  
Center Point ◽  
Degenerate Form ◽  
Point Curve ◽  
Position Synthesis ◽  
Point Form

Abstract In this paper we develop a method of characterizing the center-point curves for planar four-position synthesis. We predict the five characteristic shapes of the center-point curve using the kinematic classification of the compatibility linkage obtained from a complex number formulation for planar four-position synthesis. This classification scheme is more extensive than the conventional Grashof and non-Grashof classifications in that the separate classes of change point compatibility linkages are also included. A non-Grashof compatibility linkage generates a unicursal form of the center-point curve; a Grashof compatibility linkage generates a bicursal form; a single change point compatibility linkage generates a double point form; and a double or triple change point compatibility linkage generates a circular-degenerate or a hyperbolic-degenerate form.

scholarly journals Three-Dimensional Trajectory Construction and Observation of Group Behavior of Wild Bats During Cave Emergence

2021 ◽  
Vol 33 (3) ◽  
pp. 556-563
Author(s):  
Emyo Fujioka ◽  
Mika Fukushiro ◽  
Kazusa Ushio ◽  
Kyosuke Kohyama ◽  
Hitoshi Habe ◽  
...  
Keyword(s):  
Quantitative Estimation ◽  
Three Dimensional ◽  
Experimental System ◽  
High Sensitivity ◽  
Group Behavior ◽  
Three Dimensions ◽  
Detection And Tracking ◽  
External Objects ◽  
Behavioral Classification

Echolocating bats perceive the surrounding environment by processing echoes of their ultrasound emissions. Echolocation enables bats to avoid colliding with external objects in complete darkness. In this study, we sought to develop a method for measuring the collective behavior of echolocating bats (Miniopterus fuliginosus) emerging from their roost cave using high-sensitivity stereo-camera recording. First, we developed an experimental system to reconstruct the three-dimensional (3D) flight trajectories of bats emerging from the roost for nightly foraging. Next, we developed a method to automatically track the 3D flight paths of individual bats so that quantitative estimation of the population in proportion to the behavioral classification could be conducted. Because the classification of behavior and the estimation of population size are ecologically important indices, the method established in this study will enable quantitative investigation of how individual bats efficiently leave the roost while avoiding colliding with each other during group movement and how the group behavior of bats changes according to weather and environmental conditions. Such high-precision detection and tracking will contribute to the elucidation of the algorithm of group behavior control in creatures that move in groups together in three dimensions, such as birds.

scholarly journals Population Characteristics Erodium tataricum Willd.

2020 ◽  
Vol 6 (9) ◽  
pp. 45-52
Author(s):  
E Krylova
Keyword(s):  
Population Characteristics ◽  
Absolute Maximum ◽  
Aerial Parts ◽  
Ontogenetic Structure ◽  
Tap Root ◽  
The Absolute ◽  
Herbaceous Perennial

Erodium tataricum is a herbaceous perennial multi-headed tap-root (caudex) plant. Hemicryptophyte. Endemic. The ontogenetic structure was studied in the shrub-herb-grass petrophytic steppe. Individuals of the species have four periods and ten ontogenetic states. It was revealed that the population is normal with an incomplete spectrum. In accordance with the classification of A. A. Uranova and O. V. Smirnova the population is definitive. According to the criterion of the absolute maximum, the population is young. The ontogenetic spectrum of the population is left-sided. A specific ontogenetic spectrum corresponds to a characteristic ontogenetic spectrum, i.e. biology of the species. According to the ontogenetic spectrum, the development of the population is characterized as sustainable. The peculiarity of Erodium tataricum is that on all aerial parts of the plant there is abundant pubescence, but in the old generative ontogenetic state, pubescence on the leaves decreases. Reproduction of the species is carried out by seed. In the subsenile ontogenetic state, senile particulation is possible.

An Easy Proof for Some Classical Theorems in Plane Geometry

1992 ◽  
Vol 35 (4) ◽  
pp. 560-568 ◽  
Author(s):  
C. Thas
Keyword(s):  
Projective Plane ◽  
Projective Geometry ◽  
The Other ◽  
Plane Geometry ◽  
The Real ◽  
Easy Proof ◽  
Special Cases ◽  
Euclidean Planes ◽  
Straight Lines ◽  
Short Method

AbstractThe main result of this paper is a theorem about three conies in the complex or the real complexified projective plane. Is this theorem new? We have never seen it anywhere before. But since the golden age of projective geometry so much has been published about conies that it is unlikely that no one noticed this result. On the other hand, why does it not appear in the literature? Anyway, it seems interesting to "repeat" this property, because several theorems in connection with straight lines and (or) conies in projective, affine or euclidean planes are in fact special cases of this theorem. We give a few classical examples: the theorems of Pappus-Pascal, Desargues, Pascal (or its converse), the Brocard points, the point of Miquel. Finally, we have never seen in the literature a proof of these theorems using the same short method see the proof of the main theorem).

A Semiotic Model of Multimedia

2011 ◽  
pp. 1-21 ◽  
Author(s):  
Helen C. Purchase ◽  
Daniel Naumann
Keyword(s):  
Multimedia Communication ◽  
Model Error ◽  
Three Dimensions ◽  
Multimedia Model ◽  
Semiotic Model ◽  
Perceived Difficulty ◽  
Media Objects ◽  
Practical Investigation

Models of multimedia communication are attempts to classify the numerous types of media objects available, and to provide a basis for the use of unambiguous terminology in a new and expanding field. Many of these models are products of theory, rather then practical investigation, and few have been empirically studied to assess their suitability. This chapter firstly presents a novel multimedia model (called TOMUS) which is based on a common classification of semiotic representational systems, and uses three dimensions of sign, syntax and modality. By separating the classification of the nature of the text to be communicated from the nature of the technology or interaction, the model provides a focussed terminology for consistent and appropriate discussion about multimedia texts. The chapter also reports on an experiment which investigated the understandability of the dimensions comprising TOMUS. The experiment entailed subjects classifying various media objects according to the TOMUS model. Error and perceived difficulty data were collected; analysis of this data revealed which of the categories are the most difficult to comprehend. Suggestions are made as to the causes of these difficulties, and recommendations as to how the model might be correspondingly altered are proposed.

scholarly journals Luminosity Classification of Be Stars by Balmer Line Narrow Band Photometry

1982 ◽  
Vol 98 ◽  
pp. 37-40
Author(s):  
Wolfgang Zeuge
Keyword(s):  
Narrow Band ◽  
Balmer Line ◽  
Be Stars ◽  
The Absolute ◽  
Absolute Luminosity

The absolute luminosity of most Be stars can be determined by using Balmer line narrow band photometry with an accuracy of about 0.4 mag. The few cases in which this method fails can be detected.

Stable Lattices

1953 ◽  
Vol 5 ◽  
pp. 261-270 ◽  
Author(s):  
Harvey Cohn
Keyword(s):  
Convex Body ◽  
Finite Number ◽  
Quadratic Forms ◽  
Convex Bodies ◽  
Lattice Points ◽  
Three Dimensions ◽  
General Convex ◽  
Critical Lattice ◽  
The Absolute

The consideration of relative extrema to correspond to the absolute extremum which is the critical lattice has been going on for some time. As far back as 1873, Korkine and Zolotareff [6] worked with the ellipsoid in hyperspace (i.e., with quadratic forms), and later Minkowski [8] worked with a general convex body in two or three dimensions. They showed how to find critical lattices by selection from among a finite number of relative extrema. They were aided by the long-recognized premise that only a finite number of lattice points can enter into consideration [1] when one deals with lattices “admissible to convex bodies.”

II—The Use of Balloons in Meteorology

1957 ◽  
Vol 10 (1) ◽  
pp. 67-70 ◽  
Author(s):  
D. N. Harrison
Keyword(s):  
Heat Engine ◽  
Absolute Zero ◽  
Three Dimensions ◽  
Free Atmosphere ◽  
The Earth ◽  
Simple Instrument ◽  
The Absolute

Although early meteorological records were naturally confined to the weather experienced at the surface of the Earth, as soon as meteorology began to be a science it was realized that what went on above the surface was important and that the physics of the air needed to be studied in three dimensions. An obvious illustration is the use made of cloud observations—the nature and structure of clouds, the method of their formation and their movement. Something could be learnt on those questions by observations from the ground, aided by such a simple instrument as the nephoscope. Most people, and certainly all concerned with navigation, know that the movement of clouds may be very different from the wind at the surface. It was also realized that since the atmosphere is a heat engine a knowledge of the temperature of the upper air was required. Anyone who has climbed a mountain knows that the temperature falls, and this was confirmed for the free atmosphere by observations with kites. It was clearly of interest to know whether the fall of temperature was maintained until the absolute zero was reached, and if not, why not. It is in the measurement of temperature and wind in the upper air that balloons have found their chief use.

scholarly journals Organizational propaganda on the Internet: A systematic review

2019 ◽  
Vol 9 (1) ◽  
pp. 103-127
Author(s):  
Irina Lock ◽  
Ramona Ludolph
Keyword(s):  
Systematic Review ◽  
Public Relations ◽  
Three Dimensions ◽  
The Internet ◽  
Mutual Understanding ◽  
Digital Environment ◽  
Primary Research ◽  
Communicative Acts ◽  
Digital Channels

The digital environment alters the way organizations use propaganda and facilitates its spread. This development calls for an outline of the features of propaganda by organizations on the Internet and to reconsider where public relations (PR) stops and propaganda begins. By means of a systematic review of primary research on organizational propaganda online, we propose a definition and describe the ‘five Ws’ of digital organizational propaganda: who employs propaganda, to whom, on which channels, which media are used (where), the objectives of the propaganda strategy (why), and in which contexts it occurs (when). Contrary to the offline setting, organizations engaging in propaganda online do not hide their identity and primarily address (potential) followers with the goal to change attitudes. Based on our findings, we propose a classification of digital organizational propaganda along three dimensions: ethical versus unethical, mutual understanding versus persuasion, and direct versus indirect communication. Digital organizational propaganda is defined as the direct persuasive communicative acts by organizations with an unethical (i.e. untruthful, inauthentic, disrespectful, or unequal) intent through digital channels. Thus, this study addresses the imbalance between the growing primary research on digital propaganda, the missing definition, and the lacking systematic empirical overview of propaganda’s digital characteristics.

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