scholarly journals On one variational problem reducing to differential-boundary operator

2019 ◽  
Vol 52 (1) ◽  
Author(s):  
O. G. Storozh
Keyword(s):  
Variational Problem ◽  
Boundary Operator

Protection Zones in Periodic-Parabolic Problems

2020 ◽  
Vol 20 (2) ◽  
pp. 253-276
Author(s):  
Julián López-Gómez
Keyword(s):  
Mixed Type ◽  
Principal Eigenvalue ◽  
Boundary Operator ◽  
General Boundary ◽  
Parabolic Problems ◽  
Parabolic Operator ◽  
Protection Zones ◽  
Competitive Environments

AbstractThis paper characterizes whether or not\Sigma_{\infty}\equiv\lim_{\lambda\uparrow\infty}\sigma[\mathcal{P}+\lambda m(% x,t),\mathfrak{B},Q_{T}]is finite, where {m\gneq 0} is T-periodic and {\sigma[\mathcal{P}+\lambda m(x,t),\mathfrak{B},Q_{T}]} stands for the principal eigenvalue of the parabolic operator {\mathcal{P}+\lambda m(x,t)} in {Q_{T}\equiv\Omega\times[0,T]} subject to a general boundary operator of mixed type, {\mathfrak{B}}, on {\partial\Omega\times[0,T]}. Then this result is applied to discuss the nature of the territorial refuges in periodic competitive environments.

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 Construction of lattice Möbius domain wall fermions in the Schrödinger functional scheme

2018 ◽  
Vol 33 (01) ◽  
pp. 1850012
Author(s):  
Yuko Murakami ◽  
Ken-Ichi Ishikawa
Keyword(s):  
Perturbation Theory ◽  
Gauge Theory ◽  
Domain Wall ◽  
Beta Function ◽  
Boundary Operator ◽  
Tree Level ◽  
Domain Wall Fermions ◽  
Functional Scheme ◽  
Temporal Boundary ◽  
Optimal Type

In this paper, we construct the Möbius domain wall fermions (MDWFs) in the Schrödinger functional (SF) scheme for the SU(3) gauge theory by adding a boundary operator at the temporal boundary of the SF scheme setup. Using perturbation theory, we investigate the properties of several constructed MDWFs, including the optimal type domain wall, overlap, truncated domain wall, and truncated overlap fermions. We observe the universality of the spectrum of the effective four-dimensional operator at the tree-level, and fermionic contribution to the universal one-loop beta function is reproduced for MDWFs with a sufficiently large fifth-dimensional extent.

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.

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