Minimization of vectors of curvilinear functionals on the second order jet bundle: sufficient efficiency conditions

2011 ◽  
Vol 6 (8) ◽  
pp. 1657-1669 ◽  
Author(s):  
Ariana Pitea ◽  
Mihai Postolache
Keyword(s):  
Second Order ◽  
Jet Bundle ◽  
Efficiency Conditions

scholarly journals Sufficient Efficiency Conditions for Vector Ratio Problem on the Second-Order Jet Bundle

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Ariana Pitea
Keyword(s):  
Optimality Conditions ◽  
Mechanical Engineering ◽  
Optimization Theory ◽  
Necessary Optimality Conditions ◽  
Variational Problems ◽  
Second Order ◽  
Mechanical Work ◽  
Jet Bundle ◽  
Multiobjective Variational Problems ◽  
Efficiency Conditions

Motivated by its possible applications in mechanics and mechanical engineering, in our previous published work (Pitea and Postolache, 2011), we initiated an optimization theory for the second-order jet bundle. We considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multitime multiobjective variational problems, subject to PDE and/or PDI constraints. Within this framework, we introduced necessary optimality conditions. As natural continuation of these results, the present work introduces a study of sufficient efficiency conditions.

scholarly journals Minimization of Vectors of Curvilinear Functionals on Second-Order Jet Bundle: Dual Program Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Mihai Postolache
Keyword(s):  
Variational Problem ◽  
Necessary Conditions ◽  
Optimization Theory ◽  
General Setting ◽  
Second Order ◽  
Mechanical Work ◽  
Program Theory ◽  
Jet Bundle ◽  
Dual Program ◽  
Suitable Framework

A previous paper (2011), Pitea and Postolache, considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multitime multiobjective variational problem, subject to PDE and/or PDI constraints. They have chosen the suitable framework offered by the second-order jet bundle, and initiated an optimization theory for this class of problems by introducing necessary conditions. As natural continuation of these results, the present work introduces a dual program theory, the general setting, and the theory which is new as a whole, containing our results.

Minimization of vectors of curvilinear functionals on the second order jet bundle

2011 ◽  
Vol 6 (3) ◽  
pp. 459-470 ◽  
Author(s):  
Ariana Pitea ◽  
Mihai Postolache
Keyword(s):  
Second Order ◽  
Jet Bundle

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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