scholarly journals Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
José L. Gámez ◽  
Juan F. Ruiz-Hidalgo
Keyword(s):  
Global Shape ◽  
Bifurcation From Infinity ◽  
Resonant Problem ◽  
Dimension One

This paper is devoted to two different but related tags: firstly, the side of the bifurcation from infinity at every eigenvalue of the problem−u″(t)=λu(t)+g(t,u(t)),u∈H01(0,π), secondly, the solutions of the associated resonant problem at any eigenvalue. From the global shape of the nonlinearitygwe obtain computable integral values which will decide the behavior of the bifurcations and, consequently, the possibility of finding solutions of the resonant problems.

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

scholarly journals Nonlinear Conditions for Ultradifferentiability

2021 ◽  
Author(s):  
David Nicolas Nenning ◽  
Armin Rainer ◽  
Gerhard Schindl
Keyword(s):  
General Validity ◽  
Dimension One ◽  
Analogous Theorem

AbstractA remarkable theorem of Joris states that a function f is $$C^\infty $$ C ∞ if two relatively prime powers of f are $$C^\infty $$ C ∞ . Recently, Thilliez showed that an analogous theorem holds in Denjoy–Carleman classes of Roumieu type. We prove that a division property, equivalent to Joris’s result, is valid in a wide variety of ultradifferentiable classes. Generally speaking, it holds in all dimensions for non-quasianalytic classes. In the quasianalytic case we have general validity in dimension one, but we also get validity in all dimensions for certain quasianalytic classes.

Global precedence and response activation: Evidence from LRPs

2002 ◽  
Vol 55 (1) ◽  
pp. 289-310 ◽  
Author(s):  
Jeff Miller ◽  
David Navon
Keyword(s):  
Global Precedence ◽  
Local Shape ◽  
Global Shape ◽  
Preliminary Information ◽  
Readiness Potentials ◽  
Global Advantage ◽  
Response Activation ◽  
Lateralized Readiness Potentials

Lateralized readiness potentials (LRPs) were measured in left/right/no-go tasks using compound global/local stimuli. In Experiment 1, participants responded to local target shapes and ignored global ones. RTs were affected by the congruence of the global shape with the local one, and LRPs indicated that irrelevant global shapes activated the responses with which they were associated. In Experiment 2, participants responded to conjunctions of target shapes at both levels, withholding the response if a target appeared at only one level. Global shapes activated responses in no-go trials, but local shapes did not. The results are consistent with partial-output models in which preliminary information about global shape can partially activate responses that are inconsistent with the local shape. They also demonstrate that part of the global advantage arises early, before response activation begins and probably before recognition of the local shape.

scholarly journals Allocation of attention to biological motion: Local motion dominates global shape

2011 ◽  
Vol 11 (3) ◽  
pp. 4-4 ◽  
Author(s):  
M. Hirai ◽  
D. R. Saunders ◽  
N. F. Troje
Keyword(s):  
Biological Motion ◽  
Local Motion ◽  
Global Shape

scholarly journals Global shape processing: Which parts form the whole?

2010 ◽  
Vol 10 (6) ◽  
pp. 16-16 ◽  
Author(s):  
J. Bell ◽  
S. Hancock ◽  
F. A. A. Kingdom ◽  
J. W. Peirce
Keyword(s):  
Global Shape ◽  
Shape Processing

Unilateral Global Bifurcation from Infinity in Nonlinearizable One-Dimensional Dirac Problems

2021 ◽  
Vol 31 (01) ◽  
pp. 2150005
Author(s):  
Ziyatkhan S. Aliyev ◽  
Nazim A. Neymatov ◽  
Humay Sh. Rzayeva
Keyword(s):  
Dirac Equation ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Nontrivial Solutions ◽  
One Dimensional ◽  
Bifurcation From Infinity ◽  
The One ◽  
Nodal Properties

In this paper, we study the unilateral global bifurcation from infinity in nonlinearizable eigenvalue problems for the one-dimensional Dirac equation. We show the existence of two families of unbounded continua of the set of nontrivial solutions emanating from asymptotically bifurcation intervals and having the usual nodal properties near these intervals.

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