The general analytic expression forS4-symmetry-invariant potential functions of tetra-atomic homonuclear molecules

1985 ◽  
Vol 28 (2) ◽  
pp. 287-295 ◽  
Author(s):  
A. Schmelzer ◽  
J. N. Murrell
Keyword(s):  
Potential Functions ◽  
Invariant Potential ◽  
Analytic Expression

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

Introduction

2018 ◽  
Author(s):  
Tim Lewens
Keyword(s):  
Social Sciences ◽  
Human Nature ◽  
Potential Functions ◽  
Human Psychology ◽  
Human Culture ◽  
The Third ◽  
Current State ◽  
Large Numbers ◽  
The Social ◽  
Compare And Contrast

Many evolutionary theorists have enthusiastically embraced human nature, but large numbers of evolutionists have also rejected it. It is also important to recognize the nuanced views on human nature that come from the side of the social sciences. This introduction provides an overview of the current state of the human nature debate, from the anti-essentialist consensus to the possibility of a Gray’s Anatomy of human psychology. Three potential functions for the notion of species nature are identified. The first is diagnostic, assigning an organism to the correct species. The second is species-comparative, allowing us to compare and contrast different species. The third function is contrastive, establishing human nature as a foil for human culture. The Introduction concludes with a brief synopsis of each chapter.

Analytic expression for the charge carried by a locally excited Bloch state

2021 ◽  
Vol 103 (24) ◽  
Author(s):  
István Magashegyi ◽  
Katalin Oltyán ◽  
Péter Földi
Keyword(s):  
Locally Excited ◽  
Bloch State ◽  
Analytic Expression

scholarly journals Genome-wide identification of the CCCH gene family in rose (Rosa chinensis Jacq.) reveals its potential functions

2021 ◽  
Vol 35 (1) ◽  
pp. 517-526
Author(s):  
Cai-hua Li ◽  
Qing-xi Fang ◽  
Wen-Jing Zhang ◽  
Yu-huan Li ◽  
Jin-zhu Zhang ◽  
...  
Keyword(s):  
Gene Family ◽  
Potential Functions ◽  
Rosa Chinensis ◽  
Genome Wide

scholarly journals Determination of differential pencils with impulse from interior spectral data

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongxia Guo ◽  
Guangsheng Wei ◽  
Ruoxia Yao
Keyword(s):  
Spectral Data ◽  
Interior Point ◽  
Potential Functions ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Inverse Spectral ◽  
Differential Pencils ◽  
Second Spectrum

Abstract In this paper, we are concerned with the inverse spectral problems for differential pencils defined on $[0,\pi ]$ [ 0 , π ] with an interior discontinuity. We prove that two potential functions are determined uniquely by one spectrum and a set of values of eigenfunctions at some interior point $b\in (0,\pi )$ b ∈ ( 0 , π ) in the situation of $b=\pi /2$ b = π / 2 and $b\neq \pi /2$ b ≠ π / 2 . For the latter, we need the knowledge of a part of the second spectrum.

Stability analysis of uncertain delay differential equations

2021 ◽  
pp. 1-11
Author(s):  
Jian Wang ◽  
Yuanguo Zhu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Liu Process ◽  
Uncertain Dynamical System ◽  
Analytic Expression ◽  
Functional Differential ◽  
The One ◽  
Delay Differential

Uncertain delay differential equation is a class of functional differential equations driven by Liu process. It is an important model to describe the evolution process of uncertain dynamical system. In this paper, on the one hand, the analytic expression of a class of linear uncertain delay differential equations are investigated. On the other hand, the new sufficient conditions for uncertain delay differential equations being stable in measure and in mean are presented by using retarded-type Gronwall inequality. Several examples show that our stability conditions are superior to the existing results.

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