scholarly journals Shape Operator Metric for Surface Normal Approximation

2009 ◽  
pp. 447-461 ◽  
Author(s):  
Guillermo D. Canas ◽  
Steven J. Gortler
Keyword(s):  
Normal Approximation ◽  
Shape Operator ◽  
Surface Normal

scholarly journals Application of shape operator under infinitesimal bending of surface

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1267-1271
Author(s):  
Milica Cvetkovic ◽  
Ljubica Velimirovic
Keyword(s):  
Explicit Form ◽  
Shape Operator ◽  
Regular Surface ◽  
Infinitesimal Bending ◽  
Surface Normal ◽  
Point To Point

In case of bendable surfaces it is useful to discuss the variation of magnitudes such as the shape operator. The shape operator is a good way to measure how a regular surface S bends in R3 by valuation how the surface normal v changes from point to point. We considered the variation of shape operator under infinitesimal bending of surface given in an explicit form and its application in considering what happened with the elliptic, hyperbolic, parabolic kind of points under the infinitesimal bending of surface.

Pointwise pseudo-slant submanifolds of a Kenmotsu manifold

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5833-5853 ◽  
Author(s):  
Viqar Khan ◽  
Mohammad Shuaib
Keyword(s):  
Present Article ◽  
Warped Product ◽  
Shape Operator ◽  
Warped Products ◽  
Canonical Structure ◽  
Slant Submanifold ◽  
Kenmotsu Manifold ◽  
Slant Submanifolds ◽  
Kenmotsu Manifolds

In the present article, we have investigated pointwise pseudo-slant submanifolds of Kenmotsu manifolds and have sought conditions under which these submanifolds are warped products. To this end first, it is shown that these submanifolds can not be expressed as non-trivial doubly warped product submanifolds. However, as there exist non-trivial (single) warped product submanifolds of a Kenmotsu manifold, we have worked out characterizations in terms of a canonical structure T and the shape operator under which a pointwise pseudo slant submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

A Note on the Accuracy of Normal Approximation of Random Quantities

2021 ◽  
Vol 73 (1) ◽  
pp. 62-67
Author(s):  
Ibrahim A. Ahmad ◽  
A. R. Mugdadi
Keyword(s):  
Sample Size ◽  
Order Statistic ◽  
Normal Approximation ◽  
Order Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Limiting Distribution ◽  
Exact Order ◽  
Fixed Sample ◽  
Independent Identically Distributed

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

scholarly journals The limits of normal approximation for adult height

2021 ◽  
Author(s):  
Sergei A. Slavskii ◽  
Ivan A. Kuznetsov ◽  
Tatiana I. Shashkova ◽  
Georgii A. Bazykin ◽  
Tatiana I. Axenovich ◽  
...  
Keyword(s):  
Complex Traits ◽  
Adult Height ◽  
Normal Approximation ◽  
Classical Model ◽  
Model Complexity ◽  
Test Case ◽  
Genetic Studies ◽  
Quantitative Genetic ◽  
Profound Influence ◽  
Log Normal

AbstractAdult height inspired the first biometrical and quantitative genetic studies and is a test-case trait for understanding heritability. The studies of height led to formulation of the classical polygenic model, that has a profound influence on the way we view and analyse complex traits. An essential part of the classical model is an assumption of additivity of effects and normality of the distribution of the residuals. However, it may be expected that the normal approximation will become insufficient in bigger studies. Here, we demonstrate that when the height of hundreds of thousands of individuals is analysed, the model complexity needs to be increased to include non-additive interactions between sex, environment and genes. Alternatively, the use of log-normal approximation allowed us to still use the additive effects model. These findings are important for future genetic and methodologic studies that make use of adult height as an exemplar trait.

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