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.

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.

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.

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.

CONDUCTION AND ELECTROLYSIS IN CELLULOSE

1963 ◽  
Vol 41 (7) ◽  
pp. 1022-1035 ◽  
Author(s):  
E. J. Murphy
Keyword(s):  
Organic Semiconductors ◽  
Theoretical Expression ◽  
Voltage Gradient ◽  
Boltzmann Factor ◽  
Resonance Tunneling ◽  
Faraday’S Law ◽  
Adjacent Structures ◽  
The One ◽  
Main Component ◽  
Organic Dielectric

Dry cellulose conducts in accordance with the theoretical expression for the temperature dependence of ionic conductivity. The appearance of products of electrolysis in approximate agreement with Faraday's law and the presence of gaseous hydrogen as the main component indicate that the conduction is ionic (rather than electronic, as in organic semiconductors), and that it depends upon the migration of protons and proton holes. It is proposed that conduction in dry cellulose involves tunneling of the proton between equivalent sites, the one in the ion, the other in an adjacent neutral molecule. Resonance tunneling occurs when these structures are in suitable mutual configurations. This occurs with a frequency given by a Boltzmann factor. Experiment indicates that the energy in this factor is 10.6 kcal/mole. As this is about twice the energy of the hydrogen bond, it is proposed that the energy of activation for mobility represents the simultaneous breaking of two hydrogen bonds in bringing adjacent structures into suitable configuration for resonance tunneling. The results are considered to exhibit an example of an organic dielectric which conducts by the transport of protons at a rate depending upon an activation energy due to the breaking of hydrogen bonds.A small dependence of the molar yield of gas per Faraday on the applied voltage gradient was observed. Its significance is discussed in terms of a generalization of the electrode process to include effects of field emission as the voltage gradient approaches the breakdown level.

Discrete Kinematic Geometry in Testing Axes of Rotation of Spindles

2016 ◽  
Author(s):  
Delun Wang ◽  
Zhi Wang ◽  
Yu Wu ◽  
Huimin Dong ◽  
Shudong Yu
Keyword(s):  
Geometry Model ◽  
Displacement Sensors ◽  
Characteristic Lines ◽  
Kinematic Geometry ◽  
Fixed Axis ◽  
Global Invariants ◽  
New Perspective ◽  
Line Trajectory ◽  
Error Motion ◽  
First Time

The accuracy of actual motion of the spindle of a machine tool, a key performance index, is measured at a series of positions, and evaluated using a discrete kinematic geometry model. The kinematic geometry model, or more precisely a novel mechanism, is presented for the first time in this paper and validated using an apparatus consisting of a spindle, an artifact with double master ball and five displacement sensors as per ASME codes and standards [1]. The six kinematic parameters of the spindle with a single rotor — three translations and three rotations are obtained using the novel mechanism and the measurements. The theory of discrete kinematic geometry is employed to reveal the intrinsic properties of the trajectories traced by the characteristic lines of the rotor. In order to avoid the influences caused by the locations and directions of the measuring coordinate systems, the invariants of a discrete line-trajectory, particularly the spherical image curve and the striction curve [2], are introduced to deal with the discrete measurements. The global invariants, the approximated moving axis and the approximated fixed axis of the rotor in the error motion, independent of the assembling position of the double master balls on the rotor, are proposed to evaluate the rotational accuracy of spindles. The discrete kinematic geometry provides a new perspective and a theoretical base for assessing the accuracy of the spindle motion.

scholarly journals A study on a line congruence as surface in the space of lines

2021 ◽  
Vol 6 (10) ◽  
pp. 11109-11123
Author(s):  
Rashad A. Abdel-Baky ◽  
◽  
Monia F. Naghi ◽  
Keyword(s):  
Kinematic Geometry ◽  
Line Congruence

<abstract><p>In this work, we introduce a line congruence as surface in the space of lines in terms of the E. Study map. This provides the ability to derive some formulae of surfaces theory into line spaces. In addition, the well known equation of the Plucker's conoid has been obtained and its kinematic-geometry are examined in details. At last, an example of application is investigated and explained in detail.</p></abstract>

Kinematic geometry of a line trajectory in spatial motion

2015 ◽  
Vol 29 (9) ◽  
pp. 3597-3608 ◽  
Author(s):  
Reem A. Al-Ghefari ◽  
Rashad A. Abdel-Baky
Keyword(s):  
Spatial Motion ◽  
Kinematic Geometry ◽  
Line Trajectory
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