scholarly journals A simplification of the Agrachev–Gamkrelidze second-order variation for bang–bang controls

2010 ◽  
Vol 59 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Irad Ratmansky ◽  
Michael Margaliot
Keyword(s):  
Second Order ◽  
Order Variation

Second-order variation in Thomas-Fermi theory

1990 ◽  
Vol 41 (5) ◽  
pp. 2363-2369 ◽  
Author(s):  
S. J. Lee ◽  
S. Das Gupta ◽  
R. K. Bhaduri
Keyword(s):  
Second Order ◽  
Fermi Theory ◽  
Thomas Fermi ◽  
Order Variation

Stability of the critical equilibrium of a compressed column on a Winkler foundation

2021 ◽  
pp. 108128652110615
Author(s):  
Mingzhi Gao ◽  
Ming Jin
Keyword(s):  
Potential Energy ◽  
Energy Functional ◽  
Exact Expression ◽  
Second Order ◽  
Winkler Foundation ◽  
Critical Equilibrium ◽  
Order Variation ◽  
The Stability ◽  
Potential Energy Functional ◽  
Theoretical Results

In this paper, the critical equilibrium of a simply supported compressed column on a Winkler foundation is analyzed based on Koiter’s theory. The exact expression of the potential energy functional is presented. By the Fourier series of the disturbance deflection, the second-order variation of the potential energy is expressed as a quadratic form. At critical equilibrium, the second-order variation of the potential energy is semi-positive definite, so that the stability of the critical equilibrium is determined by the sign of the fourth-order variation or sixth-order variation. It can be seen that only in two small ranges of elastic-foundation stiffness is the corresponding critical state stable and the bifurcation equilibrium upward. Then, the theoretical results of this paper are compared with previous experimental and theoretical results.

scholarly journals Restoring Poissonian Images by a Combined First-Order and Second-Order Variation Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Le Jiang ◽  
Jin Huang ◽  
Xiao-Guang Lv ◽  
Jun Liu
Keyword(s):  
Lagrange Equation ◽  
Noise Removal ◽  
Poisson Noise ◽  
Second Order ◽  
Variational Model ◽  
Gradient Descent Method ◽  
First Order ◽  
Order Variation ◽  
Imaging Science ◽  
Blurred Images

The restoration of blurred images corrupted by Poisson noise is an important topic in imaging science. The problem has recently received considerable attention in recent years. In this paper, we propose a combined first-order and second-order variation model to restore blurred images corrupted by Poisson noise. Our model can substantially reduce the staircase effect, while preserving edges in the restored images, since it combines advantages of the first-order and second-order total variation. We study the issues of existence and uniqueness of a minimizer for this variational model. Moreover, we employ a gradient descent method to solve the associated Euler-Lagrange equation. Numerical results demonstrate the validity and efficiency of the proposed method for Poisson noise removal problem.

scholarly journals On Solvability of Certain Classes of Irregular the Second Order Variation Problems

2007 ◽  
Vol 7 (2) ◽  
pp. 32-36
Author(s):  
Yu.V. Pokornyi ◽  
◽  
Zh.I. Bakhtina ◽  
A.S. Ischenko ◽  
◽  
...  
Keyword(s):  
Second Order ◽  
Order Variation

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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