scholarly journals The Pythagorean theorem in certain symmetry classes of tensors

1962 ◽  
Vol 104 (3) ◽  
pp. 510-510 ◽  
Author(s):  
Marvin Marcus ◽  
Henryk Minc
Keyword(s):  
Pythagorean Theorem ◽  
Symmetry Classes

Pythagorean theorem

AccessScience ◽  
2015 ◽  
Keyword(s):  
Pythagorean Theorem

scholarly journals A study of curvature theory for different symmetry classes of Hamiltonian

Pramana ◽  
2021 ◽  
Vol 95 (3) ◽  
Author(s):  
Y R Kartik ◽  
Ranjith R Kumar ◽  
S Rahul ◽  
Sujit Sarkar
Keyword(s):  
Symmetry Classes ◽  
Curvature Theory

scholarly journals Universality classes of the Anderson transition in the three-dimensional symmetry classes AIII, BDI, C, D, and CI

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Tong Wang ◽  
Tomi Ohtsuki ◽  
Ryuichi Shindou
Keyword(s):  
Three Dimensional ◽  
Anderson Transition ◽  
Symmetry Classes ◽  
Universality Classes

scholarly journals Structure–function relationships of the plant cuticle and cuticular waxes — a smart material?

2006 ◽  
Vol 33 (10) ◽  
pp. 893 ◽  
Author(s):  
Hendrik Bargel ◽  
Kerstin Koch ◽  
Zdenek Cerman ◽  
Christoph Neinhuis
Keyword(s):  
Structure Function ◽  
Smart Materials ◽  
Self Assembly ◽  
Water Repellency ◽  
Cuticular Waxes ◽  
Form Complex ◽  
Symmetry Classes ◽  
Research Activities ◽  
Terrestrial Habitats ◽  
Surface Waxes

The cuticle is the main interface between plants and their environment. It covers the epidermis of all aerial primary parts of plant organs as a continuous extracellular matrix. This hydrophobic natural composite consists mainly of the biopolymer, cutin, and cuticular lipids collectively called waxes, with a high degree of variability in composition and structure. The cuticle and cuticular waxes exhibit a multitude of functions that enable plant life in many different terrestrial habitats and play important roles in interfacial interactions. This review highlights structure–function relationships that are the subjects of current research activities. The surface waxes often form complex crystalline microstructures that originate from self-assembly processes. The concepts and results of the analysis of model structures and the influence of template effects are critically discussed. Recent investigations of surface waxes by electron and X-ray diffraction revealed that these could be assigned to three crystal symmetry classes, while the background layer is not amorphous, but has an orthorhombic order. In addition, advantages of the characterisation of formation of model wax types on a molecular scale are presented. Epicuticular wax crystals may cause extreme water repellency and, in addition, a striking self-cleaning property. The principles of wetting and up-to-date concepts of the transfer of plant surface properties to biomimetic technical applications are reviewed. Finally, biomechanical studies have demonstrated that the cuticle is a mechanically important structure, whose properties are dynamically modified by the plant in response to internal and external stimuli. Thus, the cuticle combines many aspects attributed to smart materials.

The Pythagorean Theorem: The Story of Its Power and Beauty by Alfred B. Posamentier

2012 ◽  
Vol 34 (3) ◽  
pp. 84-85
Author(s):  
Pamela Gorkin
Keyword(s):  
Pythagorean Theorem

Behold! The Pythagorean Theorem via Mean Proportions

1986 ◽  
Vol 17 (5) ◽  
pp. 422
Author(s):  
Michael Hardy
Keyword(s):  
Pythagorean Theorem
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