Necessary conditions for incremental stability and the second order variations

2004 ◽  
Author(s):  
V. Fromion ◽  
G. Scorletti
Keyword(s):  
Necessary Conditions ◽  
Second Order

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

Argumentation and Reflection in Plato’s Gigantomachia (Sophist 245e6–249d5)

2018 ◽  
Vol 100 (3) ◽  
pp. 241-285
Author(s):  
Daniel Vázquez
Keyword(s):  
Necessary Conditions ◽  
Second Order ◽  
Complex Activity ◽  
Causal Relations ◽  
First Order ◽  
Theoretical Assumptions ◽  
Argumentative Strategies ◽  
New Interpretation ◽  
Argumentative Structure ◽  
The Impact

Abstract This paper argues that Plato’s gigantomachia is simultaneously concerned with first-order arguments about metaphysics and epistemology and with second-order arguments that reflect on the impact of ethical components, argumentative strategies and theoretical assumptions in the conversation. This complex argumentative structure reveals, I suggest, an organic and systematic conception of philosophy where all the elements are interdependent. This interpretation has four consequences, two at the second-order level, and two concerning the first-order arguments. First, it shows that there are methodological and ethical requirements without which philosophy is impossible. Second, it shows that the text does not refute materialism but tries to reflect the necessary conditions to consider possible the existence of incorporeal beings. Third, it argues that the text assumes a conception of knowledge where knowing something is a complex activity composed of two causal relations. Finally, it offers a new interpretation of the overall conclusion of the passage.

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