scholarly journals Construction of the destination set of a dynamic system in $\mathbb{R}^3$

2021 ◽  
Vol 25 (2(36)) ◽  
pp. 83-94
Author(s):  
D. G. Kartashov ◽  
M. S. Tairova
Keyword(s):  
Dynamical Systems ◽  
Convex Hull ◽  
Dynamic System ◽  
Differential Inclusion ◽  
Support Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Arbitrary Point ◽  
Intersection Method ◽  
Three Dimensional Space

The article proposes two algorithms for the numerical construction of the convex hull of a set in three-dimensional space using its support function. The first uses the hyperplane intersection method to find the pivot points of a set. The second one is based on the deformation function and allows you to find an arbitrary point of the convex hull of a set, which is convenient in many applications. The algorithms are compared, and asymptotic complexities are found. The application of the proposed apparatus to finding the destination set of dynamical systems is shown. The dynamic system will be based on differential inclusion.

scholarly journals On Chasles' Property of the Helicoid in Tri-Twisted Real Ambient Space

2015 ◽  
Vol 23 (2) ◽  
pp. 121-132
Author(s):  
Peter T. Ho ◽  
Lucy H. Odom ◽  
Bogdan D. Suceavă
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Arbitrary Point ◽  
Invariance Property ◽  
Elementary Property ◽  
Invariance Condition ◽  
Xixth Century ◽  
Rigidity Property ◽  
Three Dimensional Space

Abstract An elementary property of the helicoid is that at every point of the surface the following condition holds: cot θ = C · d; where d is the distance between an arbitrary point to the helicoid axis, and θ is the angle between the normal and the helicoid’s axis. This rigidity property was discovered by M. Chasles in the first half of the XIXth century. Starting from this property, we give a characterization of the so-called tri-twisted metrics on the real three dimensional space with the property that a given helicoid satisfies the classical invariance condition. Similar studies can be pursued in other geometric contexts. Our most general result presents a property of surfaces of rotation observing an invariance property suggested by the analogy with Chasles’s property.

COLORFUL SYMMETRIC IMAGES IN THREE-DIMENSIONAL SPACE FROM DYNAMICAL SYSTEMS

Fractals ◽  
2012 ◽  
Vol 20 (01) ◽  
pp. 53-60 ◽  
Author(s):  
JIAN LU ◽  
YURU ZOU ◽  
ZEYI LIU ◽  
WENXIA LI
Keyword(s):  
Dynamical Systems ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Automatic Generation ◽  
Point Of View ◽  
Density Functions ◽  
Three Dimensional Space

Functions that are invariant with respect to the tetrahedral and cubic symmetries are determined. These invariant mappings are applied to serve as the density functions for automatic generation of the colorful images with such symmetries in three dimensional space from a dynamical system's point of view.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

scholarly journals Quantitative image analysis of microbial communities with BiofilmQ

2021 ◽  
Author(s):  
Raimo Hartmann ◽  
Hannah Jeckel ◽  
Eric Jelli ◽  
Praveen K. Singh ◽  
Sanika Vaidya ◽  
...  
Keyword(s):  
Image Analysis ◽  
Microbial Communities ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Software Tool ◽  
Image Cytometry ◽  
Quantitative Image Analysis ◽  
Space And Time ◽  
Quantitative Image ◽  
Three Dimensional Space

AbstractBiofilms are microbial communities that represent a highly abundant form of microbial life on Earth. Inside biofilms, phenotypic and genotypic variations occur in three-dimensional space and time; microscopy and quantitative image analysis are therefore crucial for elucidating their functions. Here, we present BiofilmQ—a comprehensive image cytometry software tool for the automated and high-throughput quantification, analysis and visualization of numerous biofilm-internal and whole-biofilm properties in three-dimensional space and time.

scholarly journals How Can I Grab That?

i-com ◽  
2020 ◽  
Vol 19 (2) ◽  
pp. 67-85
Author(s):  
Matthias Weise ◽  
Raphael Zender ◽  
Ulrike Lucke
Keyword(s):  
Virtual Reality ◽  
User Experience ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Advantages And Disadvantages ◽  
Multiple Dimensions ◽  
Application Developers ◽  
Three Dimensional Space

AbstractThe selection and manipulation of objects in Virtual Reality face application developers with a substantial challenge as they need to ensure a seamless interaction in three-dimensional space. Assessing the advantages and disadvantages of selection and manipulation techniques in specific scenarios and regarding usability and user experience is a mandatory task to find suitable forms of interaction. In this article, we take a look at the most common issues arising in the interaction with objects in VR. We present a taxonomy allowing the classification of techniques regarding multiple dimensions. The issues are then associated with these dimensions. Furthermore, we analyze the results of a study comparing multiple selection techniques and present a tool allowing developers of VR applications to search for appropriate selection and manipulation techniques and to get scenario dependent suggestions based on the data of the executed study.

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