scholarly journals Mannheim curves with modified orthogonal frame in Euclidean 3-space

2019 ◽  
Vol 43 (2) ◽  
pp. 648-663 ◽  
Author(s):  
Mohamd Saleem LONE ◽  
Hasan ES ◽  
Murat Kemal KARACAN ◽  
Bahaddin BÜKCÜ
Keyword(s):  
Orthogonal Frame

scholarly journals On Some Curves with Modified Orthogonal Frame in Euclidean 3-Space

2018 ◽  
Vol 43 (4) ◽  
pp. 1905-1916 ◽  
Author(s):  
Mohamd Saleem Lone ◽  
Hasan ES ◽  
Murat Kemal Karacan ◽  
Bahaddin Bukcu
Keyword(s):  
Orthogonal Frame

scholarly journals Modified Roller Coaster Surface in Space

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 195 ◽  
Author(s):  
Selçuk BAŞ ◽  
Talat KÖRPINAR
Keyword(s):  
Gaussian Curvature ◽  
Mean Curvature ◽  
Roller Coaster ◽  
Orthogonal Frame

In this paper, a new modified roller coaster surface according to a modified orthogonal frame is investigated in Euclidean 3-space. In this method, a new modified roller coaster surface is modeled. Both the Gaussian curvature and mean curvature of roller coaster surfaces are investigated. Subsequently, we obtain several characterizations in Euclidean 3-space.

The orientational average of exp[2πi(h.x + k.y + l.z)]

1978 ◽  
Vol 34 (6) ◽  
pp. 955-959 ◽  
Author(s):  
J. Brosius
Keyword(s):  
Molecular Structure ◽  
A Priori ◽  
Coordinate Frame ◽  
Phase Problem ◽  
Fixed Frame ◽  
Orthogonal Frame ◽  
Unit Vectors

The unit vectors e l, e 2, e 3 form a fixed orthogonal coordinate frame. The unit vectors e l ', e 2 ', e 3 ' form a movable orthogonal frame with the same origin as the fixed frame. All orientations in space of the movable frame are assumed to be equally probable. Under these conditions the average of exp [2πi(Σ3 i,j = 1a ij e i .e ' j )] is calculated. As an application the average of exp [2πi(h.x + k.y + l.z)] is calculated where the vectors h,k,l are specified and where the magnitudes of the vectors x,y,z and the angles between them are specified. This integral is of importance in utilizing a priori knowledge of molecular structure as an aid in solving the phase problem.

scholarly journals Spin-1/2 one- and two- particle systems in physical space without eigen-algebra or tensor product

2021 ◽  
Author(s):  
Sokol Andoni
Keyword(s):  
Tensor Product ◽  
Physical Space ◽  
Cross Product ◽  
Expectation Values ◽  
Orientation Space ◽  
Geometric Objects ◽  
Vector Operator ◽  
The One ◽  
Geometric Picture ◽  
Orthogonal Frame

Abstract A novel representation of spin 1/2 combines in a single geometric object the roles of the standardPauli spin vector operator and spin state. Under the spin-position decoupling approximation it consists ofthree orthonormal vectors comprising a gauge phase. In the one-particle case the representation: (1) isHermitian; (2) shows handedness; (3) reproduces all standard expectation values, including the total one particlespin modulus 𝑆tot = √3ℏ/2; (4) constrains basis opposite spins to have same handedness; (5)allows to formalize irreversibility in spin measurement. In the two-particle case: (1) entangled pairs haveprecisely related gauge phases and can be of same or opposite handedness; (2) the dimensionality of the spinspace doubles due to variation of handedness; (3) the four maximally entangled states are naturally definedby the four improper rotations in 3D: reflections onto the three orthogonal frame planes (triplets) andinversion (singlet). The cross-product terms in the expression for the squared total spin of two particlesrelates to experiment and they yield all standard expectation values after measurement. Here spin is directlydefined and transformed in 3D orientation space, without use of eigen algebra and tensor product as in thestandard formulation. The formalism allows working with whole geometric objects instead of onlycomponents, thereby helping keep a clear geometric picture of ‘on paper’ (controlled gauge phase) and ‘onlab’ (uncontrolled gauge phase) spin transformations.

scholarly journals Evolution of space curves and the special ruled surfaces with modified orthogonal frame

2020 ◽  
Vol 5 (3) ◽  
pp. 2027-2039 ◽  
Author(s):  
Kemal Eren ◽  
◽  
Hidayet Huda Kosal
Keyword(s):  
Ruled Surfaces ◽  
Space Curves ◽  
Orthogonal Frame

Riemannian Geometry in an Orthogonal Frame

10.1142/4808 ◽  
2001 ◽  
Author(s):  
É Cartan ◽  
V V Goldberg
Keyword(s):  
Riemannian Geometry ◽  
Orthogonal Frame

Calibration of a Precision SINS IMU and Construction of IMU-bound Orthogonal Frame

2015 ◽  
Vol 24 (1) ◽  
pp. 36-48 ◽  
Author(s):  
B. A. Blazhnov ◽  
◽  
G. I. Emel’yantsev ◽  
E. V. Dranitsyna ◽  
A. P. Stepanov ◽  
...  
Keyword(s):  
Orthogonal Frame

Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science

2013 ◽  
Vol 712-715 ◽  
pp. 2464-2468
Author(s):  
Shi Heng Wang
Keyword(s):  
Local Fields ◽  
Affine Subspace ◽  
Parseval Frame ◽  
Direct Sum ◽  
Reducing Subspaces ◽  
Dilation Factor ◽  
Definition Of ◽  
Frame Wavelets ◽  
Manufacturing Science ◽  
Orthogonal Frame

Manufacturing science focuses on understanding problems from the perspective of the stakeholders involved and then applying manufacturing science as needed. We investigate semi-orthogonal frame wavelets and Parseval frame wavelets in with a dilation factor. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace.The definition of multiple pseudofames for subspaces with integer translation is proposed. The notion of a generalized multiresolution structure of is also introduced. The construction of a generalized multireso-lution structure of Paley-Wiener subspaces of is investigated.

Effect of Size and Frame of Visual Field on the Accuracy of an Aiming Movement

Perception ◽  
1997 ◽  
Vol 26 (3) ◽  
pp. 287-300 ◽  
Author(s):  
Yann Coello ◽  
Madeleine A Grealy
Keyword(s):  
Visual Field ◽  
Visual Information ◽  
Visual Scene ◽  
Visual Context ◽  
Radial Error ◽  
Field Control ◽  
On Line ◽  
Aiming Movement ◽  
Target Locations ◽  
Orthogonal Frame

The aim of this study was to analyse the effects of manipulating the size and contour of the visual field on the accuracy of an aiming task. Subjects were required to perform pointing movements without seeing their moving hand. The target was displayed in either a wide structured visual field (control condition), a narrow visual field with orthogonal frame, or a narrow visual field with circular frame. The visual information surrounding the target was always provided prior to movement onset, but during the execution of the movement on only half of the trials. Overall, the results showed that undershooting was a common performance characteristic in all of the conditions. In comparison to the control performance, an increase of the degree of undershoot was found when the target was displayed inside a narrower visual field. An additional radial error was found when the contour of the visual scene was circular, but only when the visual context was available during the movement. The same pattern of results was observed for variable error. However, angular errors were not found to vary over the different conditions. Overall, the findings suggested that the visual context contributed to the assessment of the target locations, and the subsequent motor programming. Furthermore, visual information aided the on-line control of the unseen hand, but the extent of this was dependent on the size and shape of the frame denoting the visual scene. Finally, in the absence of any unexpected perturbation, the en-route amendment of the arm trajectory, based on visual information processing, seemed to be more related to distance than azimuth control.

INVOLUTE-EVOLUTE CURVES ACCORDING TO MODIFIED ORTHOGONAL FRAME

2021 ◽  
Vol 21 (2) ◽  
pp. 385-394
Author(s):  
AYŞE ZEYNEP AZAK
Keyword(s):  
Euclidean Space ◽  
Curvature And Torsion ◽  
Orthogonal Pairs ◽  
Orthogonal Frame ◽  
Zero Points

In this paper, the involute-evolute curve concept has been defined according to two type modified orthogonal frames at non-zero points of curvature and torsion in the Euclidean space E^3 , respectively. Later, the characteristic theorems related to the distance between the corresponding points of these curves have been given. Besides, the relations have been found between the curvatures and also torsions of the two type the involute-evolute modified orthogonal pairs.

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