scholarly journals A dual form of the sharp Nash inequality and its weighted generalization

2018 ◽  
Vol 51 (1) ◽  
pp. 129-144
Author(s):  
Eric A. Carlen ◽  
Elliott H. Lieb
Keyword(s):  
Nash Inequality ◽  
Dual Form

Dynamics of a Contact Structure Along a Vector Field of its Kernel

2008 ◽  
Vol 8 (1) ◽  
Author(s):  
Abbas Bahri ◽  
Yongzhong Xu
Keyword(s):  
Vector Field ◽  
Variational Problem ◽  
Contact Structure ◽  
Contact Form ◽  
Dual Form

AbstractIn this paper we prove that in order to define the homology of [3], the hypothesis that there exists a vector field in the kernel of the contact form which defines a dual form with the same orientation is not essential. The technique is quantitative: as we introduce a large amount of rotation near the zeroes of the vector field in the kernel, we track down the modification of the variational problem and provide bounds on a key quantity (denoted by τ).

Periphrasis in Tundra Nenets1

Periphrasis ◽  
2012 ◽  
Author(s):  
Irina Nikolaeva
Keyword(s):  
Number System ◽  
Dual Form ◽  
Intransitive Verbs ◽  
Detailed Picture ◽  
Rare Instance ◽  
The Way

A detailed picture of periphrasis in Nenets (Uralic) presents a typologically rare instance of periphrasis in a nominal paradigm (as opposed to more familiar verbal periphrasis). Previous accounts treated Nenets nouns as an uncontroversial example of periphrasis, but this chapter demonstrates that a closer look reveals a more complicated picture. It argues that the choice between the usage of the periphrastic dual form and the numeral ‘two’ (which takes the singular) correlates with definiteness and/or discourse givenness. In addition, analysis of this rare instance of periphrasis in a noun system reveals interesting aspects of the way the number system works in the language. The chapter also investigates the periphrastic realization of verbal negation, where the auxiliary carries the information of the verb type. For intransitive verbs, the type is either ‘subjective’ or ‘reflexive’ and there are, surprisingly, arguments in favour of treating these as purely morphological classes.

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