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The horizontal trust region subproblem in the algorithm is only a general trust region subproblem while the vertical trust region subproblem is defined by a parameter size of the vertical direction subject only to an ellipsoidal constraint.
      
This method is different from classical algorithms in which the gray differential values of the mutual vertical direction are combined into one gradient value.
      
The stretching of a liquid sample, squeezed out in the vertical direction from an aperture of an arbitrary form, is investigated.
      
A study is made of the parametric excitation of internal waves in a continuously stratified liquid in a vessel executing oscillations in the vertical direction.
      
In [2, 3] the effect of high-frequency harmonic vibration in the vertical direction on the stability of this flow was investigated.
      
The present study investigates the pulsation motion of a cylindrical cavity near a free boundary of a liquid, allowing for displacement of the axis of the cavity in the vertical direction.
      
Taking the Coriolis force into account leads to the formation of a spiral flow structure in the vertical direction.
      
The waves are generated by a piston, i.e., a disk lying on a fixed horizontal plane and oscillating in the vertical direction.
      
The medical cabin with a patient moves to the operational position only in the vertical direction.
      
The plasma would thereby be fully covered in the vertical direction, and the total number of collimator channels would be 21 (12 channels in the radial camera and nine channels in the compact camera).
      
Analyses by culture methods showed that micromycetes were present in all peat layers and that their abundance tended to decrease with depth, except for yeasts, which were uniformly distributed in a vertical direction.
      
Analysis of sea current velocities showed that the principal flow has a southeastern horizontal direction and downward vertical direction.
      
For the sound field calculations, an approach is developed on the basis of the parabolic approximation in the horizontal plane and the mode representation in the vertical direction.
      
In the gas-dynamical flow pattern described with the "hot-line" model, a considerable fraction of the matter is accelerated in the vertical direction during the flow's interaction with the circumdisk halo.
      
Compression occurs in the plane of the pyramid base inside quantum dots, and stretching occurs along the vertical direction.
      
The picture is reversed near quantum dots: stretching occurs in the lateral direction and compression in the vertical direction.
      
Lasing in the vertical direction in InGaN/GaN/AlGaN structures with InGaN quantum dots
      
Lasing in vertical direction occurs at low temperatures, indicating ultrahigh gains (~ 105 cm-1) in the active region.
      
It is shown that hysteresis observed when a sample is probed in the vertical direction is due to the surface energy-work thermodynamic cycle.
      
Lasing in the vertical direction in quantum-size InGaN/GaN multilayer heterostructures
      
 

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