The Geometry of GF(q3)

1986 ◽  
Vol 38 (3) ◽  
pp. 672-696 ◽  
Author(s):  
F. A. Sherk
Keyword(s):  
Three Dimensional ◽  
Quadratic Extension ◽  
Galois Field ◽  
Complex Numbers ◽  
Inversive Plane ◽  
The Real ◽  
Quadric Surfaces ◽  
Cubic Surfaces ◽  
Cubic Extension ◽  
Miquelian Inversive Plane

1. Introduction. Inversive geometry involves as basic entities points and circles [2, p. 83; 4, p. 252]. The best known examples of inversive planes (the Miquelian planes) are constructed from a field K which is a quadratic extension of some other field F. Thus the complex numbers yield the Real Inversive Plane, while the Galois field GF(q2)(q = pe, p prime) yields the Miquelian inversive plane M(q) [2, chapter 9; 4, p. 257]. The purpose of this paper is to describe an analogous geometry of M(q) which derives from GF(q3), the cubic extension of GF(q).The resulting space, is three-dimensional, involving a class of surfaces which include planes, some quadric surfaces, and some cubic surfaces. We explore these surfaces, giving particular attention to the number of points they contain, and their intersections with lines and planes of the space .

Transformations depending on sets of associated points

1952 ◽  
Vol 48 (3) ◽  
pp. 383-391
Author(s):  
T. G. Room
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Three Dimensional ◽  
Cubic Curves ◽  
Birational Transformations ◽  
Quadric Surfaces ◽  
Base Points ◽  
Dimensional Projective Space ◽  
Quartic Curves

This paper falls into three sections: (1) a system of birational transformations of the projective plane determined by plane cubic curves of a pencil (with nine associated base points), (2) some one-many transformations determined by the pencil, and (3) a system of birational transformations of three-dimensional projective space determined by the elliptic quartic curves through eight associated points (base of a net of quadric surfaces).

Robot Assisted Modal Analysis on a Stationary Bladed Wheel

2014 ◽  
Author(s):  
L. Bertini ◽  
B. Monelli ◽  
P. Neri ◽  
C. Santus ◽  
A. Guglielmo
Keyword(s):  
Three Dimensional ◽  
Laser Doppler Vibrometer ◽  
Testing Time ◽  
Real Representation ◽  
The Real ◽  
Complex Formulation ◽  
Frequency Matching ◽  
Input Multiple Output ◽  
Multiple Measurements ◽  
Single Input

This paper shows an automated procedure to experimentally find the eigenmodes of a bladed wheel with highly three-dimensional geometry. The stationary wheel is supported in free-free conditions, neglecting stress-stiffening effects. The single input / multiple output approach was followed. The vibration speed was measured by means of a laser-Doppler vibrometer, and an anthropomorphic robot was used for accurate orientation and positioning of the measuring laser beam, allowing multiple measurements during a limited testing time. The vibration at corresponding points on each blade was measured and the data elaborated in order to find the initial (lower frequency) modes. These modal shapes were then compared to finite element simulations and accurate frequency matching and exact number of nodal diameters obtained. Being the modes cyclically harmonic, the complex formulation could be attractive, being not affected by the angular phase of the mode representation. Nevertheless, stationary modes were experimentally detected, rather than rotating, and then the real representation was necessary. The discrete Fourier transform of the blade displacements easily allowed to find both the angular phase and the correct number of nodal diameters. Successful MAC experimental to analytical comparison was finally obtained with the real representation after introducing the proper angular phase for each mode.

The Lω1ω1-theory of hilbert spaces

1967 ◽  
Vol 32 (3) ◽  
pp. 295-304 ◽  
Author(s):  
Ralph Kopperman
Keyword(s):  
Hilbert Spaces ◽  
Predicate Calculus ◽  
Complex Numbers ◽  
The Real ◽  
Elementary Class

It will be shown later in this paper that the class of all Hilbert spaces is not an elementary class (in the wider sense) in the lower predicate calculus. It is not difficult to find a type and a sentence in Lω1ω1 (of that type) whose models are precisely the Hilbert spaces (slightly altered to include in their domains the real or complex numbers).

scholarly journals Real-Life Continuous Flash Suppression - Rendering The Real World Unconscious Using Augmented Reality Goggles

2018 ◽  
Author(s):  
Uri Korisky ◽  
Rony Hirschhorn ◽  
Liad Mudrik
Keyword(s):  
Augmented Reality ◽  
Real World ◽  
Three Dimensional ◽  
Real Life ◽  
Continuous Flash Suppression ◽  
Future Studies ◽  
The Real ◽  
Dominant Eye ◽  
Novel Variant ◽  
Real Objects

Notice: a peer-reviewed version of this preprint has been published in Behavior Research Methods and is available freely at http://link.springer.com/article/10.3758/s13428-018-1162-0Continuous Flash Suppression (CFS) is a popular method for suppressing visual stimuli from awareness for relatively long periods. Thus far, it has only been used for suppressing two-dimensional images presented on-screen. We present a novel variant of CFS, termed ‘real-life CFS’, with which the actual immediate surroundings of an observer – including three-dimensional, real life objects – can be rendered unconscious. Real-life CFS uses augmented reality goggles to present subjects with CFS masks to their dominant eye, leaving their non-dominant eye exposed to the real world. In three experiments we demonstrate that real objects can indeed be suppressed from awareness using real-life CFS, and that duration suppression is comparable that obtained using the classic, on-screen CFS. We further provide an example for an experimental code, which can be modified for future studies using ‘real-life CFS’. This opens the gate for new questions in the study of consciousness and its functions.

scholarly journals Fractional Newton-Raphson Method

2021 ◽  
Vol 8 (1) ◽  
pp. 1-13
Author(s):  
A. Torres-Hernandez ◽  
F. Brambila-Paz
Keyword(s):  
Fractional Calculus ◽  
Iterative Method ◽  
Complex Numbers ◽  
Initial Condition ◽  
The Real ◽  
Complex Roots ◽  
Newton Raphson ◽  
Roots Of A Polynomial ◽  
Raphson Method

The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n, with n ∈ N. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractional calculus, which we will call the Fractional Newton-Raphson (F N-R) Method, which has the ability to enter the space of complex numbers given a real initial condition, which allows us to find both the real and complex roots of a polynomial unlike the classical Newton-Raphson method.

scholarly journals XRSISE: An XR Training System for Interactive Simulation and Ergonomics Assessment

2021 ◽  
Vol 2 ◽  
Author(s):  
Michail Pavlou ◽  
Dimitrios Laskos ◽  
Evangelia I. Zacharaki ◽  
Konstantinos Risvas ◽  
Konstantinos Moustakas
Keyword(s):  
Virtual World ◽  
Three Dimensional ◽  
Cost Effective ◽  
Knowledge Retention ◽  
Training System ◽  
Human Model ◽  
Interactive Simulation ◽  
Industrial Training ◽  
The Real ◽  
Physical Constraints

The use of virtual reality (VR) techniques for industrial training provides a safe and cost effective solution that contributes to increased engagement and knowledge retention levels. However, the process of experiential learning in a virtual world without biophysical constraints might contribute to muscle strain and discomfort, if ergonomic risk factors are not considered in advance. Under this scope, we have developed a digital platform which employs extended reality (XR) technologies for the creation and delivery of industrial training programs, by taking into account the users and workplace specificities through the adaptation of the 3D virtual world to the real environment. Our conceptual framework is composed of several inter-related modules: 1) the XR tutorial creation module, for automatic recognition of the sequence of actions composing a complex scenario while this is demonstrated by the educator in VR, 2) the XR tutorial execution module, for the delivery of visually guided and personalized XR training experiences, 3) the digital human model (DHM) based simulation module for creation and demonstration of job task simulations avoiding the need of an actual user and 4) the biophysics assessment module for ergonomics analysis given the input received from the other modules. Three-dimensional reconstruction and aligned projection of the objects situated in the real scene facilitated the imposition of inherent physical constraints, thereby allowed to seamlessly blend the virtual with the real world without losing the sense of presence.

scholarly journals The Real Era of the Art of Medicine Begins with Artificial Intelligence (Preprint)

2019 ◽  
Author(s):  
Bertalan Meskó
Keyword(s):  
Artificial Intelligence ◽  
Digital Health ◽  
Medical Science ◽  
Three Dimensional ◽  
Three Dimensional Printing ◽  
The Real ◽  
Art Of Medicine ◽  
Health Technologies ◽  
Based Medicine ◽  
Dimensional Printing

UNSTRUCTURED Physicians have been performing the art of medicine for hundreds of years, and since the ancient era, patients have turned to physicians for help, advice, and cures. When the fathers of medicine started writing down their experience, knowledge, and observations, treating medical conditions became a structured process, with textbooks and professors sharing their methods over generations. After evidence-based medicine was established as the new form of medical science, the art and science of medicine had to be connected. As a result, by the end of the 20th century, health care had become highly dependent on technology. From electronic medical records, telemedicine, three-dimensional printing, algorithms, and sensors, technology has started to influence medical decisions and the lives of patients. While digital health technologies might be considered a threat to the art of medicine, I argue that advanced technologies, such as artificial intelligence, will initiate the real era of the art of medicine. Through the use of reinforcement learning, artificial intelligence could become the stethoscope of the 21st century. If we embrace these tools, the real art of medicine will begin now with the era of artificial intelligence.

scholarly journals RESONANCES ON HEDGEHOG MANIFOLDS

2013 ◽  
Vol 53 (5) ◽  
pp. 416-426 ◽  
Author(s):  
Pavel Exner ◽  
Jiří Lipovský
Keyword(s):  
Real Axis ◽  
Quantum Particle ◽  
Single Point ◽  
Three Dimensional ◽  
High Energy ◽  
Quantum Graphs ◽  
The Real ◽  
Momentum Plane ◽  
Embedded Eigenvalues ◽  
Aharonov Bohm

We discuss resonances for a nonrelativistic and spinless quantum particle confined to a two- or three-dimensional Riemannian manifold to which a finite number of semiinfinite leads is attached. Resolvent and scattering resonances are shown to coincide in this situation. Next we consider the resonances together with embedded eigenvalues and ask about the high-energy asymptotics of such a family. For the case when all the halflines are attached at a single point we prove that all resonances are in the momentum plane confined to a strip parallel to the real axis, in contrast to the analogous asymptotics in some metric quantum graphs; we illustrate this on several simple examples. On the other hand, the resonance behaviour can be influenced by a magnetic field. We provide an example of such a ‘hedgehog’ manifold at which a suitable Aharonov-Bohm flux leads to absence of any true resonance, i.e. that corresponding to a pole outside the real axis.

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