Kinematic geometry of hyperbolic dual spherical motions and Euler–Savary’s equation

2020 ◽  
Vol 17 (05) ◽  
pp. 2050079
Author(s):  
Nadia Alluhaibi ◽  
R. A. Abdel-Baky
Keyword(s):  
Kinematic Geometry ◽  
Point Trajectories ◽  
The One ◽  
Differential Properties ◽  
Planar Motions ◽  
Explicit Expressions

In this paper, differential properties of the one-parameter hyperbolic dual spherical kinematics are developed with explicit expressions independent of coordinates systems. We calculate Euler–Savary equations of spherical kinematics in the dual Lorentzian 3-space [Formula: see text]. Then from E. Study’s map new proofs are directly attained for the Disteli’s formulae and their spatial equivalents are examined in detail. Lastly for spherical and planar motions, the point trajectories theoretical expressions of the point trajectories are investigated with a certain value of acceleration and velocity, which are regarded as different forms of Euler–Savary equation form.

On the one-parameter Lorentzian spatial motions

2019 ◽  
Vol 16 (12) ◽  
pp. 1950197 ◽  
Author(s):  
Nadia Alluhaibi ◽  
R. A. Abdel-Baky
Keyword(s):  
Theoretical Expression ◽  
Kinematic Geometry ◽  
Line Congruence ◽  
The One ◽  
Line Trajectory ◽  
Differential Properties ◽  
Explicit Expressions

In this paper, differential properties of the one-parameter Lorentzian spatial motions are developed with explicit expressions independent of coordinates systems. In term of this, we calculate the Disteli formulae of a spacelike line trajectory and derive the connections with kinematic geometry of the axodes. Lastly, a theoretical expression of a spacelike inflection line congruence are investigated in detail.

The one-way information deficit for a class of two-qubit states

2015 ◽  
Vol 13 (02) ◽  
pp. 1550012
Author(s):  
H. Eftekhari ◽  
E. Faizi
Keyword(s):  
Dynamic Behavior ◽  
Quantum States ◽  
Parameter Family ◽  
General Quantum ◽  
The One ◽  
Qubit States ◽  
Additional Assumptions ◽  
Explicit Expressions

So far, one-way information deficit (OWID) has been calculated explicitly only for Bell-diagonal states and the four-parameter family of X-states with additional assumptions and expressions for more general quantum states are not known. In this paper, we derive explicit expressions for OWID for a larger class of two-qubit states, namely, a five-parameter family of two-qubit states. The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID is more robust against the decoherence than the entanglement.

Fine-Tuning Geometrically Constrained Planar Motions

2011 ◽  
Author(s):  
Ping Zhao ◽  
Q. J. Ge ◽  
Feng Gao ◽  
Hai-Jun Su
Keyword(s):  
Standard Deviation ◽  
Kinetic Energy ◽  
Reference Frames ◽  
Distance Measure ◽  
Fine Tuning ◽  
Planar Motion ◽  
Motion Error ◽  
Point Trajectories ◽  
Geometrically Constrained ◽  
Planar Motions

This paper presents a method for fine-tuning a geometrically constrained planar motion in the context of motion approximation. It builds on the recent work that seeks to identify and extract point trajectories of an explicitly given planar motion. Once two point trajectories are obtained, the remaining issue is to determine the length of the “coupler link” that connects the two point trajectories such that the resulting motion best approximates the original motion. In this paper, the concept of standard deviation in statistics and probability theory is used to define the “distance” between two planar motions. This distance definition is bi-invariant with respect to the choice of both moving and fixed reference frames. Furthermore, the concept of kinetic energy is also used for combining translation with rotation when calculating the distance between two planar displacements. A simple, direct search method for obtaining the optimum length of the coupler link is presented that minimizes the standard deviation of the motion error in terms of the kinetic energy based distance measure for planar displacements.

Realizations of chiral transformations: explicit forms

1970 ◽  
Vol 48 (19) ◽  
pp. 2272-2282 ◽  
Author(s):  
John M. Charap
Keyword(s):  
Pseudoscalar Meson ◽  
General Problem ◽  
The Other ◽  
Field Theories ◽  
Meson Field ◽  
Nonlinear Functions ◽  
The One ◽  
Nonlinear Realizations ◽  
Explicit Expressions

The parallel approaches to the general problem of giving nonlinear realizations of chiral SU(n) [Formula: see text]SU(n) appropriate to phenomenological field theories as derived by Callan, Coleman, Wess, and Zumino on the one hand, and by Barnes and Isham on the other, are reviewed and compared. Explicit expressions are given for the nonlinear functions of the pseudoscalar meson field variables which arise in these methods.

A sextic primal in five dimensions

1950 ◽  
Vol 46 (1) ◽  
pp. 91-105 ◽  
Author(s):  
E. M. Hartley
Keyword(s):  
Fourth Order ◽  
Five Dimensions ◽  
Four Dimensions ◽  
Independent Functions ◽  
The Subject ◽  
The One ◽  
Considerable Detail ◽  
Explicit Expressions

In a recent tract (Baker (1)) there is described in considerable detail a configuration of forty-five points which are nodes of a quartic primal in four dimensions. The geometry of this primal is very fascinating; among its interesting properties is the fact that a number of well-known geometrical configurations, which usually arise as unrelated phenomena, here all appear in connexion with the one figure. The interest of the primal, of course, lies chiefly in the large number of collineations which leave it invariant. The group G* of these collineations is considered in a paper by Burkhardt (2), in which are given explicit expressions for five algebraically independent functions of the five variables, which are left invariant by the operations of the group. The simplest of these invariants is of the fourth order, and when equated to zero represents the quartic primal which is the subject of Baker's tract.

scholarly journals MÉTODOS PARA TRANSFORMAR COEFICIENTES ZERNIKE AL VARIAR LA PUPILA DE UN SISTEMA ÓPTICO ABERRADO METHODS TO TRANSFORM ZERNIKE COEFFICIENTS WHEN THE PUPIL OF AN ABERRATED OPTICAL SYSTEM VARIES

Anales AFA ◽  
2010 ◽  
pp. 60-68
Author(s):  
S. A. Comastri ◽  
L. I. Perez ◽  
G. D. Pérez ◽  
G. Martin ◽  
A. Bianchetti
Keyword(s):  
Optical System ◽  
Analytical Method ◽  
Analytical Methods ◽  
Graphical Method ◽  
Wavefront Aberration ◽  
Zernike Polynomials ◽  
Field Point ◽  
The One ◽  
Explicit Expressions

The wavefront aberration for a given field point is often expanded in Zernike polynomials and varies when pupil is modified. In many cases the coefficients pattern corresponding to a pupil is known and one needs to calculate the one for a rotated, contracted or decentred pupil. In this paper we review the most important concepts which we present in recent articles concerning the development of an analytical and a graphical method to carry out this transformation. Using our analytical method we find explicit expressions for the elements of a matrix which transforms Zernike coefficients of up to 7th order computed for a circular original pupil into those corresponding to a contracted, decentred and rotated new pupil. Our graphical method is useful to identify qualitatively new coefficients in terms of original ones or vice versa for any order of Zernike´s expansion. As an example, we show an application of both methods. Finally, we synthesize some works of other authors which develop numerical or analytical methods for the coefficients conversion and we compare their more relevant results to ours.

scholarly journals Hypothesis testing and advanced distinguishers in differential cryptanalysis of block ciphers

2015 ◽  
Vol 64 (1) ◽  
pp. 217-231 ◽  
Author(s):  
Theodosis Mourouzis ◽  
Nicolas Courtois
Keyword(s):  
Hypothesis Testing ◽  
Random Permutation ◽  
Block Ciphers ◽  
General Hypothesis ◽  
Random Samples ◽  
Observable Variable ◽  
Finite Set ◽  
The One ◽  
Differential Properties ◽  
Truncated Differential

Abstract Distinguishing distributions is a major part during cryptanalysis of symmetric block ciphers. The goal of the cryptanalyst is to distinguish two distributions; one that characterizes the number of certain events which occur totally at random and another one that characterizes same type of events but due to propagation inside the cipher. This can be realized as a hypothesis testing problem, where a source is used to generate independent random samples in some given finite set with some distribution P, which is either R or W, corresponding to propagation inside the cipher or a random permutation respectively. Distinguisher’s goal is to determine which one is most likely the one which was used to generate the sample. In this paper, we study a general hypothesis-testing based approach to construct statistical distinguishers using truncated differential properties. The observable variable in our case is the expected number of pairs that follow a certain truncated differential property of the form ΔX → ΔY after a certain number of rounds. As a proof of concept, we apply this methodology to GOST and SIMON64/128 block ciphers and present distinguishers on 20 and 22 rounds respectively.

On the generalizations of the polar inertia momentum of the closed curves obtained kinematically

2005 ◽  
Vol 42 (1) ◽  
pp. 73-78
Author(s):  
S. Yüce ◽  
M Düldül ◽  
N. Kuruoğu
Keyword(s):  
Closed Orbit ◽  
Closed Curves ◽  
The One ◽  
Planar Motions

In this paper we give some general results for the polar inertia momentums, given by [2], of the closed orbit curves obtained during the one-parameter closed planar motions.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

Nucleation of Disorder in Fe3Al Alloys

1967 ◽  
Vol 25 ◽  
pp. 312-313
Author(s):  
P. R. Swann ◽  
W. R. Duff ◽  
R. M. Fisher
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Annealing Temperature ◽  
Antiphase Domain ◽  
Effect Of Temperature ◽  
Domain Structures ◽  
Transmission Electron ◽  
Domain Boundaries ◽  
Higher Temperature ◽  
The One

Recently we have investigated the phase equilibria and antiphase domain structures of Fe-Al alloys containing from 18 to 50 at.% Al by transmission electron microscopy and Mössbauer techniques. This study has revealed that none of the published phase diagrams are correct, although the one proposed by Rimlinger agrees most closely with our results to be published separately. In this paper observations by transmission electron microscopy relating to the nucleation of disorder in Fe-24% Al will be described. Figure 1 shows the structure after heating this alloy to 776.6°C and quenching. The white areas are B2 micro-domains corresponding to regions of disorder which form at the annealing temperature and re-order during the quench. By examining specimens heated in a temperature gradient of 2°C/cm it is possible to determine the effect of temperature on the disordering reaction very precisely. It was found that disorder begins at existing antiphase domain boundaries but that at a slightly higher temperature (1°C) it also occurs by homogeneous nucleation within the domains. A small (∼ .01°C) further increase in temperature caused these micro-domains to completely fill the specimen.

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