scholarly journals Geometric Invariants of Normal Curves under Conformal Transformation in $\mathbb{E}^3$

2021 ◽  
Vol 53 ◽  
Author(s):  
Mohamd Saleem Lone
Keyword(s):  
Conformal Transformation ◽  
Sufficient Condition ◽  
Normal Curve ◽  
Geometric Invariant ◽  
Geometric Invariants ◽  
Invariant Properties

In this paper, we investigate the geometric invariant properties of a normal curve on a smooth immersed surface under conformal transformation. We obtain an invariant-sufficient condition for the conformal image of a normal curve. We also find the deviations of normal and tangential components of the normal curve under the same motion.

Biorthogonalization, geometric invariant properties and rate-based estimate of Lyapunov spectra

2005 ◽  
Vol 342 (5-6) ◽  
pp. 421-429 ◽  
Author(s):  
A. Adrover ◽  
F. Creta ◽  
M. Giona ◽  
M. Valorani
Keyword(s):  
Geometric Invariant ◽  
Lyapunov Spectra ◽  
Invariant Properties

On Some Geometric Invariants Associated to the Space of Flat Connections on an Open Space

1996 ◽  
Vol 39 (2) ◽  
pp. 169-177
Author(s):  
I. Biswas ◽  
K. Guruprasad
Keyword(s):  
Moduli Space ◽  
Symplectic Structure ◽  
Open Space ◽  
Geometric Invariant ◽  
Flat Connections ◽  
Geometric Invariants ◽  
Marked Surface

AbstractA geometric invariant is associated to the parabolic moduli space on a marked surface and is related to the symplectic structure of the moduli space.

scholarly journals CONFORMAL AND PARACONTACTLY GEODESIC TRANSFORMATIONS OF ALMOST PARACONTACT METRIC STRUCTURES

2020 ◽  
Vol 35 (1) ◽  
pp. 121
Author(s):  
Adara-Monica Blaga
Keyword(s):  
Conformal Transformation ◽  
Tensor Field ◽  
Structure Tensor ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Tensor Fields ◽  
Kenmotsu Manifold ◽  
Metric Structures ◽  
Necessary And Sufficient

We give the expressions of the virtual and the structure tensor fields of an almost paracontact metric structure. We also introducethe notion of paracontactly geodesic transformation and prove thatthe structure tensor field is invariant under conformal andparacontactly geodesic transformations. For the particular case of para-Kenmotsu structure, we give a necessary and sufficient condition for a conformal transformation to map it to an $\alpha$-para-Kenmotsu structure and show that a para-Kenmotsu manifold admits no nontrivial paracontactly geodesic transformation of the metric. In the conformal case, the virtual tensor field is invariant.  

Hyperbolic worldsheets and worldlines of null Cartan curves in de Sitter 3-space

2021 ◽  
pp. 2150026
Author(s):  
Qingxin Zhou ◽  
Jingbo Xu ◽  
Zhigang Wang
Keyword(s):  
Singularity Theory ◽  
Close Relation ◽  
Dual Relationships ◽  
Normal Curve ◽  
De Sitter ◽  
Geometric Invariant ◽  
Geometric Properties ◽  
Hyperbolic Quadric ◽  
Cuspidal Edge

The hyperbolic worldsheets and the hyperbolic worldline generated by null Cartan curves are defined and their geometric properties are investigated. As applications of singularity theory, the singularities of the hyperbolic worldsheets and the hyperbolic worldline are classified by using the approach of the unfolding theory in singularity theory. It is shown that under appropriate conditions, the hyperbolic worldsheet is diffeomorphic to cuspidal edge or swallowtail type of singularity and the hyperbolic worldline is diffeomorphic to cusp. An important geometric invariant which has a close relation with the singularities of the hyperbolic worldsheets and worldlines is found such that the singularities of the hyperbolic worldsheets and worldlines can be characterized by the invariant. Meanwhile, the contact of the spacelike normal curve of a null Cartan curve with hyperbolic quadric or world hypersheet is discussed in detail. In addition, the dual relationships between the spacelike normal curve of a null Cartan curve and the hyperbolic worldsheet are described. Moreover, it is demonstrated that the spacelike normal curve of a null Cartan curve and the hyperbolic worldsheet are [Formula: see text]-dual each other.

The Current Situation in Chemical Stabilization of Biological Materials

1972 ◽  
Vol 30 ◽  
pp. 132-133
Author(s):  
John H. Luft
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Osmium Tetroxide ◽  
Molecular Level ◽  
Cross Linking ◽  
Chemical Stabilization ◽  
Specimen Preparation ◽  
Sufficient Condition ◽  
Radio Telescopes

With information processing devices such as radio telescopes, microscopes or hi-fi systems, the quality of the output often is limited by distortion or noise introduced at the input stage of the device. This analogy can be extended usefully to specimen preparation for the electron microscope; fixation, which initiates the processing sequence, is the single most important step and, unfortunately, is the least well understood. Although there is an abundance of fixation mixtures recommended in the light microscopy literature, osmium tetroxide and glutaraldehyde are favored for electron microscopy. These fixatives react vigorously with proteins at the molecular level. There is clear evidence for the cross-linking of proteins both by osmium tetroxide and glutaraldehyde and cross-linking may be a necessary if not sufficient condition to define fixatives as a class.

Computational Micrograph Registration with Sieve Processes

1996 ◽  
Vol 54 ◽  
pp. 440-441
Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Spatial Organization ◽  
Spatial Arrangement ◽  
Stereo Image ◽  
Image Model ◽  
Geometric Invariants ◽  
Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

The Normal Curve and its Abnormalities

1969 ◽  
Vol 14 (1) ◽  
pp. 10-11
Author(s):  
ERNEST G. POSER
Keyword(s):  
Normal Curve

The Subnormal Area Under the Normal Curve of Intelligence

1968 ◽  
Vol 13 (1) ◽  
pp. 19-21
Author(s):  
PAUL R. DOKECKI
Keyword(s):  
Normal Curve

On the construction of orthogonal curvilinear grids for regional oceanic modeling: algorithm and user guide

2020 ◽  
Vol 48 (4) ◽  
pp. 45-111
Author(s):  
A. F. Shepetkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Elliptic Problem ◽  
Software Package ◽  
Conformal Transformation ◽  
Iterative Procedure ◽  
Geometric Shape ◽  
Curvilinear Grids ◽  
Grid Points ◽  
Grid Nodes

A new algorithm for constructing orthogonal curvilinear grids on a sphere for a fairly general geometric shape of the modeling region is implemented as a “compile-once - use forever” software package. It is based on the numerical solution of the inverse problem by an iterative procedure -- finding such distribution of grid points along its perimeter, so that the conformal transformation of the perimeter into a rectangle turns this distribution into uniform one. The iterative procedure itself turns out to be multilevel - i.e. an iterative loop built around another, internal iterative procedure. Thereafter, knowing this distribution, the grid nodes inside the region are obtained solving an elliptic problem. It is shown that it was possible to obtain the exact orthogonality of the perimeter at the corners of the grid, to achieve very small, previously unattainable level of orthogonality errors, as well as make it isotropic -- local distances between grid nodes about both directions are equal to each other.

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