scholarly journals Some topics in differential geometry of normed spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Vitor Balestro ◽  
Horst Martini ◽  
Ralph Teixeira
Keyword(s):  
Differential Geometry ◽  
Minimal Surfaces ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Inner Product ◽  
Normed Spaces ◽  
Smooth Norm ◽  
Bonnet Theorem ◽  
Three Dimensional Space

AbstractFor a surface immersed in a three-dimensional space endowed with a smooth norm instead of an inner product, one can define analogous concepts of curvature and metric. With such concepts in mind, various questions immediately appear. The aim of this paper is to propose and answer some of those questions. In this framework we prove several characterizations of minimal surfaces in normed spaces, and respective analogues of some global theorems (e.g., Hadamard-type theorems) are also derived. A result on the curvature of surfaces having constant Minkowskian width is given, and finally we study the ambient metric induced on the surface, proving an extension of the classical Bonnet theorem.

Quasi-bound state calculations for several types of potential in one-, two-, and three-dimensional systems, using perturbative techniques

1993 ◽  
Vol 71 (3-4) ◽  
pp. 133-141 ◽  
Author(s):  
M. R. M. Witwit
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Energy Levels ◽  
Three Dimensional ◽  
Bound State ◽  
Inner Product ◽  
Model Potentials ◽  
Three Dimensional Space ◽  
Quasi Bound State

The energy levels of the Schrödinger equation for various model potentials in one-, two-, and three-dimensional space are calculated using the hypervirial and inner product methods.

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>

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