Weakened Hypotheses for the Variational Problem Considered by Hestenes

1965 ◽  
Vol 3 (3) ◽  
pp. 418-423 ◽  
Author(s):  
T. Guinn
Keyword(s):  
Variational Problem

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).

scholarly journals Overlap Problems on the Circle

2013 ◽  
Vol 45 (03) ◽  
pp. 773-790
Author(s):  
S. Juneja ◽  
M. Mandjes
Keyword(s):  
Variational Problem ◽  
Decay Rate ◽  
Positive Constant ◽  
The Other ◽  
The Impact ◽  
Independent And Identically Distributed

Consider a circle with perimeter N > 1 on which k < N segments of length 1 are sampled in an independent and identically distributed manner. In this paper we study the probability π (k,N) that these k segments do not overlap; the density φ(·) of the position of the disks on the circle is arbitrary (that is, it is not necessarily assumed uniform). Two scaling regimes are considered. In the first we set k≡ a√N, and it turns out that the probability of interest converges (N→ ∞) to an explicitly given positive constant that reflects the impact of the density φ(·). In the other regime k scales as aN, and the nonoverlap probability decays essentially exponentially; we give the associated decay rate as the solution to a variational problem. Several additional ramifications are presented.

Encoding in the presence of penalties. First variational problem

2020 ◽  
pp. 53-75
Author(s):  
Roman V. Belavkin ◽  
Panos M. Pardalos ◽  
Jose C. Principe ◽  
Ruslan L. Stratonovich
Keyword(s):  
Variational Problem
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