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\( Z_{ \alpha '} \le Q_{ \alpha }\)
In this chapter, we conclude the proof of the main theorem by considering the anti-symmetric case: where...
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On the Usefulness of the Vector Field Singular Points Shapes for Classification
The objects’ features play significant role in the machine learning classification. The present paper proofs and validates that the shapes of vector...
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Alpha Power Exponentiated Pareto Distribution
AbstractIn this paper, we have proposed alpha power exponentiated Pareto distribution for lifetime data to introduce a new class of alpha power...
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Animal Shapes, Modal Analysis, and Visualization of Motion (I): Horse and Camel
Eigenfunctions and eigenvalues of physical systems and engineering structures can reveal many of the system’s fundamental features and, therefore,...
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Fitting cylinders computation with an application to measuring 3D shapes
This paper observes a fitting cylinders problem for 3 D shapes. The method presented defines two cylinders that fit well with the shape considered....
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Shapes and recession cones in mixed-integer convex representability
Mixed-integer convex representable (MICP-R) sets are those sets that can be represented exactly through a mixed-integer convex programming...
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Two results about the Sackin and Colless indices for phylogenetic trees and their shapes
The Sackin and Colless indices are two widely-used metrics for measuring the balance of trees and for testing evolutionary models in phylogenetics....
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The effects of internal forces and membrane heterogeneity on three-dimensional cell shapes
The shape of cells and the control thereof plays a central role in a variety of cellular processes, including endo- and exocytosis, cell division and...
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The Measurement and Analysis of Shapes
A de Rham p -current can be viewed as a map (the current map) between the set of embeddings of a closed p -dimensional manifold into an ambient n -manifo...
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A linear technique for designing optimal rotated shapes
In this article, a simple linear method is established for designing optimal revolving objects with desired physical properties. First, the problem...
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Animal Shapes, Modal Analysis, and Visualization of Motion (II): Dynamics and Fourier Decomposition
This paper begins with solving the linear elastodynamic equation with forcing by expanding it into Fourier series. We then proceed to prove the...
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Asymptotic shapes for stationary first passage percolation on virtually nilpotent groups
We study first passage percolation (FPP) with stationary edge weights on Cayley graphs of finitely generated virtually nilpotent groups. Previous...
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The Shapes of Violin
The article has its inspiration in the analysis of the geometric shape of the violin, observing its evolution over the centuries: the current shape...
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Optimum Shapes of Supercavitating Hydrofoils at Zero Cavitation Number
AbstractWe investigate the problem of the flow around a supercavitating hydrofoils at zero cavitation number. Making use of formulas for the lift and...
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On length measures of planar closed curves and the comparison of convex shapes
In this paper, we revisit the notion of length measures associated to planar closed curves. These are a special case of area measures of...
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Hive geometry shapes the recruitment rate of honeybee colonies
Honey bees make decisions regarding foraging and nest-site selection in groups ranging from hundreds to thousands of individuals. To effectively make...
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Is it possible to use Discontinuous Shapes in Hydrodynamics?
The naval engineering has reached a high degree of sophistication. The need for the improvements of the shapes of ships, propellers, and artifacts is...
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Shape Analysis by Computing Geodesics on a Manifold via Cubic B-splines
When a parameterized probability density function is used to represent a landmark-based shape, the shape can be viewed as a point on the manifold...
